The New Model Army
The "new modelling" of Parliament's army was first proposed by Sir William Waller after his defeat at Cropredy Bridge in June 1644. Parliament's armies were recruited from regional associations but soldiers were often reluctant to campaign away from their local areas, as Waller found to his cost when trying to control his mutinous London regiments. Waller proposed the formation of a national army with no regional affiliations and the idea was taken up by Oliver Cromwell in a speech to the House of Commons in December 1644. The Self-denying Ordinance was hurried through the Commons to sweep away the existing military high command and the New Model Army Ordinance was passed on 17 February 1645.

Organisation
Parliament's new army was planned to comprise 22,000 men: twelve regiments of foot of 1,200 men each in the proportion two-thirds musketeers, one-third pikemen; eleven regiments of horse of 600 men each, one regiment of 1,000 dragoons (mounted infantrymen) and an artillery train of 50 guns. The cavalry were mainly veterans drawn from the armies of Manchester, Essex and Waller. The infantry included some veterans, with a majority of pressed men drawn from London, the east, and south-east. In Kent, some of the pressed men mutinied and had to be forcibly restrained. Parliament's intention was to enforce strict discipline in return for regular pay — eight pence per day for the infantry and two shillings per day for the cavalry, who had to supply their own horses and pay for their upkeep.
The infantry regiments wore coats of venetian red with facings to identify the individual regiments. They were armed with matchlock muskets and pikes. The cavalry wore "lobster-tail" iron headpieces and chest armour over a thick leather "buff coat". The troopers were armed with a sword and two pistols.
Sir Thomas Fairfax was appointed captain-general and commander-in-chief of the army in January 1645, with Philip Skippon as major-general of foot. Oliver Cromwell was officially appointed lieutenant-general of horse (and second-in-command of the army) in June 1645. Fourth in rank of the general officers was Thomas Hammond, lieutenant-general of ordnance, who commanded the artillery and engineers. Other officers on the general staff were charged with particular departments such as the administration of military justice and the acquisition of supplies and provisions. One of the most important of these was the scoutmaster-general Leonard Watson, who was responsible for reconnaissance and collecting intelligence on enemy movements: the efficiency of the New Model Army's intelligence department was a major factor in its success.
First Campaigns
At the time of its formation, the New Model was one of several Parliamentarian armies active in England. There was also the Scottish Covenanter army under Lord Leven, the Northern Association army under Major-General Sydenham Poyntz, formed from troops formerly commanded by Lord Ferdinando Fairfax in Yorkshire, and the Western Association army of Wiltshire and the four western counties, commanded by the Presbyterian Edward Massie. Besides these, there were smaller bodies of troops in Wales, the eastern counties and the midlands.
Although it was derided by Royalists (and some Parliamentarians) as the "New Noddle", Fairfax quickly moulded the New Model Army into an efficient, disciplined fighting force with an unusually high degree of motivation. Officers were appointed and promoted on merit rather than on their status in society. Several high-ranking officers of the New Model were from humble origins, for example Colonel Pride had been a brewer, Colonel Hewson a shoemaker.
Within months of its formation, the New Model inflicted a decisive defeat on the Royalists at the battle of Naseby in June 1645, and brought the First Civil War to an end the following year. The smaller Parliamentarian armies were either disbanded or absorbed into the New Model and in July 1647, Fairfax was made commander-in-chief of all Parliament's forces in England and Wales.
Levellers & Agitators
After the ending of the First Civil War, the Presbyterian faction in Parliament misguidedly attempted to disband the New Model Army without first settling arrears of pay, guaranteeing indemnity from prosecution for actions carried out under orders or making any provision for the relief of wounded soldiers, war widows and orphans. This led to the appointment of Agitators amongst the troops to lobby for soldiers' rights and the politicisation of the Army during 1647. For a brief period, representatives of the common soldiers sat alongside the Grandees of the high command to debate the future constitution of England at the Putney Debates in October and November 1647.
...We were not a mere mercenary army, hired to serve any arbitrary power of a state, but called forth and conjured by the several declarations of Parliament to the defence of our own and the People's just Rights and Liberties..From The Representation of the Army 1647
After the Second Civil War in 1648, radical Army officers forcibly purged Parliament of the King's supporters and brought about his trial and execution for inflicting a second war upon the nation, leading to the establishment of a republican Commonwealth in England from 1649-53. The political influence of the Leveller movement grew amongst the rank-and-file of the army from 1647 and reached crisis point during 1649 when the Leveller mutinies were suppressed by Fairfax and Cromwell.
Commonwealth & Protectorate
Under Cromwell's leadership, the army invaded Ireland in 1649 to defeat the Royalists and subjugate the Irish Catholics in retribution for the uprising against Protestant settlers in 1641. The infamous atrocities at Drogheda and Wexford took place during this campaign. The New Model Army also suffered its only major defeat and greatest number of casualties in a single military action at the storming of Clonmel in May 1650.
When Fairfax declined to lead the army against Charles II in an invasion of Scotland, Cromwell was appointed commander-in-chief in his place, leading the New Model to victory over the Scots and Royalists at the battles of Dunbar and Worcester (1650-1), which finally brought the civil wars to an end.
The role of the Army was crucial in upholding the constitutional experiments of the 1650s when most people in England wanted a return to Monarchy. In particular, the Rule of the Major-Generals (1655-7) during Oliver Cromwell's Protectorship left deep resentment and fear of military dictatorship. The expense of maintaining a standing army in England as well as armies of occupation in Scotland and Ireland was also a major drain on the financial resources of the Commonwealth and Protectorate.
At the beginning of the Anglo-Spanish War (1655-60), new units were formed from existing New Model regiments for an expedition to the West Indies, which resulted in the seizure of Jamaica from Spain in 1655. As a condition of Cromwell's military alliance with France, contingents of the New Model Army fought alongside the French in Flanders, and played a decisive role in Marshall Turenne's victory over the Spaniards at the battle of the Dunes (1658) and the capture of Dunkirk, which was ceded to England.
Oliver Cromwell's unassailable hold on power during the Protectorate was upheld by the loyalty of the New Model Army. Richard Cromwell, who succeeded Oliver in 1658, had no association with the Army and did not command the respect that his father had won in battle. Richard insisted upon retaining the title of commander-in-chief in an attempt to keep control of the Army but republican opponents of the Protectorate worked actively to spread discontent amongst the soldiers. Richard was deposed by a military junta headed by Lieutenant-General Fleetwood in April 1659 and the Commonwealth was briefly restored. However, Parliament's attempt to curb the power of the Army resulted in its forced dissolution by Major-General Lambert in October 1659.
General Monck, commander of the army occupying Scotland, disapproved of the coup and demanded the return of Parliament as the only legally-constituted government. Lambert marched his forces north to oppose Monck in December 1659 but his troops were reluctant to fight their comrades in the northern army. Lambert's forces dispersed when Monck marched from Coldstream for London in January 1660 to restore the Long Parliament as constituted before Pride's Purge of 1648. The Long Parliament was succeeded by the pro-Royalist Convention Parliament in April 1660 which authorised the Restoration of the Stuart monarchy.
The Restoration
The Convention passed an act in August 1660 ordering the disbandment of the entire New Model Army. As a special concession, Monck's regiment was scheduled to be the last to disband, but in January 1661 the regiment was active in suppressing a sudden insurrection by Fifth Monarchists in London. The order for disbandment was promptly repealed. On 14 February 1661, the regiment paraded on Tower Hill where the soldiers symbolically laid down their weapons — and with them their association with the New Model Army and the "Good Old Cause". They were immediately ordered to take up arms again as troops of King Charles II's new standing army.
From 1670, Monck's Regiment of Foot was known as the Coldstream Regiment of Foot Guards, and later the Coldstream Guards, in honour of the march that brought about the Restoration. It remains the oldest regular regiment in continuous service in the British army and is the only direct link to the New Model Army. The Grenadier Guards and the Life Guards, formed by the exiled Charles II in Flanders, are ranked as senior regiments to the Coldstream Guards.
Sources:
Godfrey Davies, The Restoration of Charles II, 1658-60 (San Marino 1955)
C.H. Firth, Cromwell's Army (London 1902)
S.R. Gardiner, History of the Great Civil War vol. ii (London 1889)
Ronald Hutton, The British Republic 1649-60 (Basingstoke 2000)