It has the attraction of simplicity, but the problem is, the cost would be absolutely horrendous if you wanted to pay the universal income at a level that would allow everyone to live comfortably: In order to pay for it, you'd risk having to tax people who are working at such a a high level that could make many people seriously question whether it's worth their while working when, after tax, they end up getting so little more than they'd get on UBI anyway.
I'm also not sure about the ethics of UBI: We already have enough of a problem in the UK with a culture of entitlement. Do we really want to go further down the road of creating a system in which everyone expects that the state (for which read: All other taxpayers) will provide them with free money without demanding anything in return?
Personally, for people below retirement age, I'd much rather see some kind of system that gives everyone the opportunity for a decent living - but always with the expectation that it's a two-way street: If you want the state to provide for you, then you have to make some effort in return. In practice that would probably mean replacing many current benefits with some kind of guaranteed job doing community work for anyone who wants one.
If you set it as £350/month (so the same as UC) that would be £4,200 per year, however with housing benefits retained that would likely be just enough to live.
With tax then paid on anything above this, those earning £12,000 would still be better off by about £1,800 if tax remained at 20%. However you probably wouldn't, you may increase that to around 25%,. At 25% tax that would cut the uplift to £1,200, however would mean that someone earning £36,000 was no better off and those earning just below the 40% rate (and all those above) would be about £700 a year worse off (change it to 24% and the break even point shifts to £45,000 and those above this are only marginally worse off, there's scope to adjust the percentage rate a little, for example at 24.5% to lower the break even point and tax those higher up a little more than at 24%).
By doing away with a LOT of paperwork (which is very costly to government) for a lot of benefits, especially for those in work benefits or carer's allowances, it may not be all that more expensive overall. It would also simplify payroll, as everyone is taxed the same rate from £0 until they hit the 40p tax rate. It would also mean that it would mostly always be worth working more as you'd be keeping about 75p from every £1 earned (although those on housing benefits may see less than this).
The main exceptions would be when childcare costs come into play or if you did a few extra hours but on an extra day (say you did a 7 hour day normally but then worked 9 hours across two days) as you may not cover your extra travel costs. (I'm sure that there's other cases, however these would likely be reasonably infrequent).
An alternative option would be to set it at about £7,000 (so the same as maternity pay), so someone on £12,000 would be £2,900 better of with a tax rate of 34%, and the break even point being about £33,000, to stop those on £50,000 being about £2,400 worse off on that tax rate you may then lower the 2% NIC threshold (or lower it quite a bit and up the NIC rate a bit above that), or fine tune the tax rate down a little.
For instance cut the 2% band from £50,000 to £33,000 but increase it to 3% would put someone on £50,000 £850 a year worse off, and someone earning £100,000 a year £1,500 worse off.