The independence of any newly elected member of parliament only exists up to the first day, from then on he/she forms political alliances in order to further their own agenda, therefore your 635(?) independent MP's would soon form parties of sorts for the life of the parliament on a tit for tat basis. My solution is to reduce the number of MP's to a more manageable number, vote for one third of them on day zero, the second third would join on day zero plus 2 years and the last third on day zero plus 4 years. By the time we get to day zero plus 6 years the first third are coming up for re-election and that's when the political horsetrading and promises would really begin. That is of course for England only, the Scots, Welsh and Northern Irish would have their own systems all under the umbrella of a federal government placed centrally (somewhere like Liverpool?)