We wouldn't need money for most benefits any more (pensions, income support, etc) so that's about £120bn of the £240bn found immediately. You mention the NHS - we'd be able to spend a lot less on that if people didn't have poverty-induced health problems, so there's another £35bn (assuming a 30% reduction of the £110bn). It's not unreasonable to assume that the difference of £85bn would essentially pay for itself by increasing the tax revenue from people spending their basic income. over time the country's GDP and tax revenue would increase due to people being better off (they go hand-in-hand).
This could well be cost neutral for the UK.