I know politics can be more emotive than analytical but I'm not sure what people want really.
Westminster is where the UK parliament is, yes it's a bit of a bubble but so is Washington DC, so is Brussels, that's the nature of cities with physical parliaments.
Politicians don't really need to be 'in touch' with the entire country, they should legislate based on data, reports, debate and of course whatever they put in their manifesto and forward plan. Most legislation is created and developed by technocrats not politicians anyway, MP's are just the faces, essentially the PR people.
If people are so against being run by Westminster then where do you want the parliament? Do you really want more local elections? Because there doesn't seem to be a big appetite for local democracy when you look at council elections, European elections, PCC elections.
We could go down the route of federalism and regional devolution. I think that could be a good thing if it energises and politicises people more but I'm not sure it would really.
Edit to say I agree parliament needs more diversity if that's what people mean by 'out of touch', even then though I think this idea of being 'in touch' is largely an illusion. Politics should be about aggregates, doing what's best for the entire country, not about individuals, not about understanding the concerns of every individual.