The back of the numbers estimates make it sufficiently obvious that the claim that these costs are a miniscule fraction of the additional cost of a UBI for UBIers arguing otherwise to have never attempted to produced a comprehensive overview. Assessing whether people are looking for work is relatively expensive in terms of administrator time, for example. But the administration system ensures that only 2% of the working age public actually get that benefit, not 100% of the population (or even the 20-30% of working age people who aren't economically active but aren't actively looking for work either). There's a reason nobody's doing studies to understand whether you could cover [most of] the costs of paying a benefit to 100% of the population by removing some of the admin staff that check the eligibility of the 2% currently receiving it, and it's the same reason perpetual motion machines aren't tested.

The existence of eligibility criteria ensures that unemployment benefits are, in normal times, paid out to only a small fraction of the population, because only a small proportion of the population is unemployed and looking for work. Eligibility testing admin isn't cheap, but it certainly isn't more expensive just paying everyone. For comparison purposes, according to it's own stats the entire DWP admin bill is in the region of £6b, including all admin for all types of benefit to all ages of people and a typically overpriced new govt IT project. Even if UBI could get that down to zero which it clearly can't, it wouldn't pay for many people to receive a UBI.