The average taxpayer with income between £20k and £30k pays on average £2630 tax, some 10.7%. If you hand him over £15k and them tax him on average additional £15k then his tax rate must be around 44%. This will be extremely demotivational. A hard-working person will have barely more than absolute freeloader and if he tries to work extra hard you will take half of his reward.

No, he will have almost twice as much money as the freeloader.

More importantly, if both him & the freeloader are spending £15k on rent & food, then the freeloader has £0k of disposable income and the worker has infinitely more disposable income.

Another way of looking at it is that average taxpayer with UBI has an income of between £35k and £45k and has a marginal rate not much different from what people making £45k are paying right now. People making £45k aren't currently significantly demotivated by taxes, are they?

You are contradicting yourself.

"the average taxpayer would pay £15k extra in taxes if they receive £15k in BI"

vs

"Another way of looking at it is that average taxpayer with UBI has an income of between £35k and £45k".

Today a taxpayer with median income £21k takes home £19k net. After your reform, he will take home the same £19k net (remember: pay £15k extra in taxes if they receive £15k in BI). Except hew will now be way below the median and making only £4k more than the now ubiquitous dude Lebowski type.

The average taxpayer is well above £21k -- that's the median income, which includes the 40% not paying taxes and of course median is well below average due to tail effects.