@izzythepush,
The Agitators of the New Model Army wanted a written constitution (they were largely Diggers, Levelers and religiously, Independents). (By the way, they called themselves Agitators, it's not an historical label.) They called it the
Agreement of the People. However, when presented by the Agitators and Levelers at the Putney Debates in October, 1647, it was unacceptable to the "Grandees"--Cromwell, Ireton and Fairfax, supported by most of the other high ranking officers of the Army. Eventually, although increasingly unpopular with the majority of the English at the time, the Grandees suckered the Army represntatives into holding three separate rendezvous, which allowed Grandees to use loyal troopers to round up the "ringleaders," many of whom were hanged. This resulted in a near mutiny of the Army in the Corn Husk Field incident. But the Grandees, the Major Generals, succeeding in imposing their will, and although other versions of the Agreement of People were proposed in coming years, it was a dead issue.
I suggest to you that Powers that were and are in England don't want to see a written constitution. Limits their options, you know.