It simplifies our overly-complex and bureaucratic welfare system considerably, and although we'd end up paying more welfare, it'd be less open to abuse and far more equitable.
This isn't an anti-welfare-state proposal. I love the welfare state, and I've seen it do a lot of good when I was growing up. It is, however, needlessly complex, expensive to administer, and open to abuse.
I'd like to see a /universal/ "citizen's allowance"-type-scheme (quite how to integrate non-British citizens into it – or whether to do so at all – is something I have no real opinion on) where every man, woman and child in the country gets an allowance based on a small number of easily-defined and hard-to-evade criteria. At it's simplest, ~4K for a child (in trust to their parents, I guess), 6K for a full-time student, ~9K per adult. This allowance would increase in line with inflation.
All other benefits, tax credits, student loans, etc. could be replaced with this extremely simple scheme. They cost around 200bn annually at the moment, I believe? A universal allowance would be more like 6-900bn with the rates mentioned above, which is significantly more, but taxes on earned income could be increased – the personal tax allowance could be abolished completely, and the lower income tax rate increased – maybe the higher income tax rate as well (it should definitely stay higher than the lower rate, of course).