I would also insert a trapdoor that future changes to the voting system would require the approval of >50% of eligible voters, including non-voters. Yes, I know Parliament cannot bind its successors and all that, but at least I can make it look bad to change it again.
Does this solve any of the immediate problems? No. Does it solve the dysfunctionality since 2008? I think so, especially given that polling these days looks like five parties getting 20% of the vote each. Labour themselves came to power on 38% of the vote.