It's an interesting question. these are just a few random thoughts..
Governments would probably be less stable because all the MPs who want to rebel against the party line but currently don't have the bottle would be able to do so. Prime Ministers would be in a weaker position.
There'd probably be more secret deals being done, more US style lobbying, more corruption.
MPs would never be accountable to the constituents or anyone else for how they voted. You could potentially have someone stand as a labour MP because the constituency had a massive labour majority, who then went on to vote with the tories on every single issue.