During this whole period of 1603-60, and particularly during the Interregnum (the period between 1649 and 1660), there were changes in the composition of the House of Commons - to its numbers, methods of selection, and areas represented.
In 1603 there were 462 Members in the Commons - 90 knights of the shire from the counties and 372 burgesses (town representatives) from the boroughs. The number had increased to 507 at the time of the Long Parliament in 1640 as further boroughs had been given the right by royal charter to return Members. The Civil War and Pride's Purge drastically reduced the numbers sitting in the Commons and there were only just about 200 Members who sat in the Rump Parliament, while the Nominated Assembly had only 144 selected Members.
The Instrument of Government
The Protectorate Parliaments were elected under the terms of the Instrument of Government, which incorporated many of the reforms proposed in 1647-8 by a radical group within the Army called the Levellers.
The distribution of seats was reorganised to give preference to county representation rather than borough seats - 259 knights of the shire compared to 141 burgesses. And the right to vote for county Members, the franchise, was extended to all men (women were still not included) who owned land or personal property worth £200.
Scotland and Ireland
In addition, Cromwell's conquests in 1649-51 had effectively, and unwillingly, annexed Ireland and Scotland to the regime in Westminster. This was reflected in the two Parliaments of 1654-8, where up to 30 representatives, largely Cromwell's followers, from each of Scotland and Ireland also sat - well before the Acts of Union of 1707 (Scotland) or 1801 (Ireland).
All these brief experiments - increased number of county seats, demotion of borough seats, a wider county franchise, and Scottish and Irish representation - were abandoned in their entirety at the Restoration which in this, as in so many other matters, wished to turn back the clock to before 1640.