Sir William Waller:
At the outbreak of the English Civil War, Sir William Waller was appointed Colonel for Parliament and in 1643 promoted to Major General and as the head of an army in the South West and later the South East, wasn't specifically known for his cavalry, (unlike Cromwell, who's personal regiment of horse within the Eastern Association has been well documented). Waller was one of the driving forces of the reforms that led to the formation of the New Model Army. Ironically this was where Waller's military career ended.
A full history can be found here: http://en.wikipedia.org/wiki/William_Waller
An English Civil War era regiment of Horse:
Over the years our ethos, image and discipline (although, not necessarily our politics!) has become based on that of New Model Army "Ironsides" and as such, more military and uniform in appearance than a traditional harquebusier of the period.
The Oxford Blues, our late 17th Century alter ego:
They origated from a New Model Army regiment of horse. Following the English Civil Wars the regiment was based in London, with Sir Arthur Haselrig as it's colonel. After the restoration in 1660 of Charles II, they became the "Earl of Oxford's Regiment", this was in recognition of Oxford's loyalty during the Civil Wars, (for which he was imprisoned at the Tower of London). Due to their blue coats rather than the red associated with The Army, the regiment was nicknamed "the Oxford Blues" and later just "The Blues". In 1685 the regiment fought at the Battle of Sedgemoor for King James II, which brought an end to the Monmouth Rebellion.
In 1750 the regiment still more commonly known as The Blues, became the "Royal Horse Guards" and it wasn't until 1969 that they were amalgamated with the Royal Dragoons to form the Blues and Royals. The Blues and Royals along with The Life Guards make up the Household Cavalry as we know it today and they are still distinguished by their blue coats. Despite centuries of being a Royal regiment they are still sometimes referred to by their counterparts in the Life Guards as "those bloody parliamentarians" in reference to their lineage that dates back to the New Model Army.