Nintecore has the newer Tiki with a side UV light (365nm, £22 on heinnie, so just over your budget), similar design you will find from RovyVon (don't know what wavelength their UV has, they are available from heinnie, but they are way over your budget)
Maybe worth checking these out.
I own a MecArmy SG5 (not really budget), the UV is extremely weak and pretty much useless.
I also own a Nitecore Tube UV and it is ok (to check bank-notes). Also, they are dirt cheap (I paid less than $10).
@chines keychain light you have found
Personally, I have not had any luck with off-brand flashlights, especially not Chinese ones (but there is always a first). I like that it has a reflector, which is why I probably would give this one a shot. But only if you are willing to throw that £20 pound light into the bin, because chances that it delivers are not that high.
@Nitecore Tube + review
I would say for the price, the review is very positive as the light does perform fairly well (also remember that it is a 4 years old review, so the last comment is probably no longer an issue). I will try to remember and check my tubes at home (I have 3, and at least 1 is still working after way over 2 years). With CFP reviews you have to always remember that they are absolute snobs there.
Personally, I would think that the tube is your best option.