Sorry to be po-faced (not to mention predictable), but 'broken' is another of those vague terms that stop people communicating effectively. As long as we talk about the NHS being 'on its knees' and the economy 'dropping off a cliff' nobody knows what anyone else is talking about, which probably makes politicians of all stripes happy.
I'm not sure if this answers the question, but I think the welfare state and tax system both need a radical overhaul, that there should be a publicly expressed (and preferable shared) vision about rights and responsibilities of all citizens, and I'd like to see a proper citizens' contract so that it is clear what is expected of everyone and what they can expect to get back in return.
None of that is 'tinkering', and I don't know how it can be done, really, as it would inevitable mean huge disruption to many people's lives.