The New Model Army was formed in February 1645 and for the most part troops and officers came from the various armies within Parliaments forces. Whilst press gangs were not used in the first place when a shortage of troops willing to fight in a National Army (rather than an association based on an area) impressment was introduced. The idea of a National Army was to achieve two aims, to allow it to take the fight to Royalist forces where ever they were gathered rather than only fight within a set area and usually for a set period but also to make it a professional army. For the first and only time until modern day, ability came before rank in commanding within the army. For this to work the Self Denying Ordinance was brought in, this disallowed Members of Parliament command within the Army. This was to remove high ranking and incompetent Gentry from positions that otherwise they would retain and thus continue the cycle of failed campaigns and missed opportunities. Cromwell was famously allowed to take a position within the army and became Commander of the Horse. Ireton his Son in Law also was allowed to serve despite being a Member of the Commons (two other Members of Parliament were also allowed to serve as local commanders on rolling three month commissions). Whilst Parliament found it fairly easy to form the basis of the army, paying and clothing it was another matter indeed. Parliament was skint, having to pay for the Scottish Army was draining the coffers and equipping a new army was causing a great deal of difficulty. Just then a great storm forced a Vatican ship into a Parliament controlled harbour. It's cargo included enough Red Cloth to clothe the whole army which Parliament seized along with the ship. The colour was obviously red and for a time was called Venetian Red (though it is doubtful it is the same colour as today's Venetian Red).
Whilst the New Model Army was disbanded after the restoration in 1660 the tradition of the Infantry wearing Red was kept. So the Iconic Redcoats of Waterloo have more than a passing nod at the Army that was key to the overthrow of the Monarchy.