Abolish the lords.
Give every MP say £200k per year that they can't have themselves but can donate to whatever party they belong to. Then ban all parties from receiving any funding from any other source - no business donations, billionaires or unions.
This would obviously cost the state a few million in now funding all the parties. But the amounts saved in corruption and wonky decisions to benefit their paymasters would be many, many times greater.
Startup parties would need to be allowed to fundraise however they could - otherwise they'd never get any money without any MPs. There would need to be a cut-off, say 10 MPs, where they're not allowed any more donations from elsewhere. Or they just need to make a choice between state or donation funded - all or nothing, you can't have both.
But whatever the answer, corrupt greedy politicians are never going to want to stop corrupt, greedy politicians from getting richer. The foxes are in charge of the henhouse so it will probably never change because they all know it's wrong but want it to stay that way.