The Coldstream Guards is the second oldest Regiment of the British Army and was founded in February 1645 and is well known for it's ceremonial duties at Buckingham Palace. This is rather ironic given it's beginnings.
The clue was in the date the regiment was formed, February 1645 was the formation of the New Model Army and the beginning of the Redcoats. Originally this was just one of the twelve foote regiments of the NMA and fought at Naseby which lead to the Kings surrender and eventual execution. From here the Regiment served in the subjection of Ireland and then in 1650 George Monck was given command and was used in the campaign against Scotland. Monck was soon to become known for his ruthless methods, both in keeping the Scotts under the cosh but also within his own Regiment. By 1660 Cromwell was dead and Richard his son (Tumbledown Dick) had failed to maintain order and Charles Fleetwood had reinstated Parliament. Monck and many others felt that the only way to bring lasting order to England was the reinstatement of the Monarchy, which Monck entered into secret negotiations with Charles. Monck had been sent back to Scotland to block Charles Stuart King of Scotland (Later King Charles II) from progressing into England by the Lord Protector. Monck choose a spot with a large stream running in front of his positions, the stream was known as Coldstream.
Monck had no intention of stopping Charles progress as he had gained assurances for the Country and himself. Charles knew he needed support within the Protectorate to gain the Thrown and Country so Monck went from enemy to Master of the Kings Horse and raised to a Duke. The Regiment was originally called The Coldstreamers but when they were raised to Guard status they changed their name again. Monck died in 1670 after serving the new King faithfully for 10 years which is the year the Coldstreamers became the Coldstream Guard.
An artists impression of the Coldstreamers laying down it's arms in 1661 and swearing allegiance to the new King of England. This image post dates the period probably by 100 - 150 years based on the dress of the musket. In reality the trousers would have been more baggy. Also note the pike have different coloured trousers on, this was not the norm, but possibly correct if dressed for the occasion though I suspect not. I also question the colours as I do not know of a green background with red cross but do not know if the original colours were replaced with the Protective.