It would be a contempt of Parliament to either request or agree to such an arrangement [1]. If you have definitive evidence of this having happened in the recent past, you really should pass it on to the Parliamentary Commissioner for Standards.

[1] https://erskinemay.parliament.uk/section/5023/corruption-or-...

This is why it’s a donation to the party - not to them or their office - although they can want a campaign contribution, which again doesn’t count as going to them.

I’ve had an MP literally solicit this from me - he emailed a bunch of local businesses basically stating his price list. He’s no longer an MP, or in politics - but you see this stuff everywhere, all the time. Any member’s bill you see has almost certainly been sponsored.

Does that include the lobbyist's cut, or would you go directly to the MP? But how much do you really gain from buying a single MP?

MPs typically move in packs ("areas" or "currents", that may or may not be officially organized around a thinktank or club), so buying the right MP you can actually move several of them. And then your representative goes and trades favors with the colleagues in government - "I'll vote for your controversial legislation if you pull that other lever over there". Representative democracy is a big sausage factory: in go blood and guts, out comes "edible" rules that society will live on.