Firstly, a UBI needs to coexist with effective controls on the cost of essentials: shelter, food, fuel, communication - health and social services too, where these are not socialised already. Otherwise the power relationships enforced by the blessed market will ensure that money returns to the owners of these resources (see housing benefit, private sector).
Secondly, without some kind of wealth tax, a UBI will entrench inequality. Property owners and inheritors of mini-trust funds might enjoy a comfortable life on a basic income level which would leave people lacking independent means struggling to make their rent.
Thirdly (especially if the first point is inadequately addressed) a UBI does not mean you can dispense with a safety net - unless you are prepared for people to suffer a great deal more than they do under the current (UK) system. People in work will tend to adjust their expenditure to the total of their UBI + earnings. If they lose their job they may not be able to make immediate cutbacks. Of course workers (income supplementers?) could be compelled to take out insurance - this would have to be better managed than it was in recent experience. A UBI doesn't discriminate in terms of need - additional needs would either have to be addressed socially (as with healthcare) or through a supplementary benefits system.
Fourthly, until you can have a universal UBI you probably need to decide what you want to do about immigration.
None of these obstacles are insurmountable - but they are significant.
As an aside, in the UK we already have a kind of bare bones UBI, for pensioners, for children and - with working tax credits, for the self-employed (who can claim whilst declaring very low levels of income). The last of these will be lost under universal credit (a UK in-and-out of work benefit, not a true UBI), where the self-employed must demonstrate minimum earnings levels if they are not to be coerced into further jobseeking.
Lastly, the cost of benefits delivery in the UK is about 5% of expenditure. Admin savings under UBI would be significant, but not game-changing.
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