In a strict legal sense, the biggest differences I'm aware of is that the candidate of a registered party are allowed to choose to use the name, description and emblem of their party on their ballot paper, but must be issued a certificate from the party's nominating officer to do so (which effectively means they must be selected following the party's own selection procedure). See here for party candidates versus here for independents.
In a practical sense, since the House of Commons sets its own rules via the will of the majority, the major parties (particularly the big two of the Conservative party and the Labour Party) have control over who takes jobs such as Speaker & Deputy speaker, as well as the membership of the various committees and even who gets the nicer offices. Similarly (somewhat obviously) the Prime Minister will not be an independent MP, and the Leader of Her Majesty's Loyal Opposition will come from the largest party not in government.
In a soft sense, party MPs are generally expected to adhere to the party line on all major issues, both in their public comments and their voting record, and a significant amount of parliamentary party work can go into achieving this. However, given that the only punishments are a reduction in party seniority, or removal of the whip (i.e., throwing them out), this doesn't always follow.