Red, I actually agree with most of the things you've mentioned, but I think you need a bit more information to go on because they're not all well thought-through. Like someone else said, due to the benefit cap, moving people out of central London wouldn't necessarily save any money even without taking opportunity costs into account, like moving people away from places they - or at least their children when they're grown - might be able to find work into places they probably won't.
And moving social housing tenants out of central London to private rentals elsewhere - there isn't enough social housing and there isn't the space to build enough because London has a hell of a lot of people compared to the rest of the UK - would also cost more.
The thing with espousing ideas like getting rid of housing benefit and tax credits completely, which do make sense in the long term and I understand why some people might want that, is what do the people who need those things do in the short term? The choices really are limited if you're already working all the hours you can or if you can't work at all due to a disability, and that's only two examples.
It would be lovely if nobody needed benefits, but we have to deal with the world we live in, not the one we want.
And even if you (hypothetical you - I'm not saying anyone here thinks this way) didn't care if loads of people ended up begging on the street and turning to crime for a couple of years until things settled down, wouldn't that also have long-term effects?
Tax credits are also different to simply raising the minimum wage. They take account of the fact that raising children or having a disability costs more - working on a minimum wage as a healthy 19-year-old male with no dependants is very obviously different to doing the same job once you have kids or a disability, both of which usually limit the hours you can work.
Most wealthy countries have tax credits of some sort, although they might have to be claimed back at the end of the year when you file your taxes (even the US has this and it's actually in some ways more generous than ours); the UK was unusual when it didn't have a system that allowed for extra responsibilities or dependants. Fighting against having tax credits is fighting against having something that most countries think is normal.