Interesting question.
If you want to, anybody can register for self-assessment in the UK and fill in a tax return. (Take care to do it right!) In all likelihood, HMRC will de-register for the following year if there is no point.
Proof of tax paid is shown on P60's for employment and pensions, official DWP letters for state pension and interest certificates for bank or building society interest. In fact, all sources of income have to provide proof of tax deducted. (There are other sources of income I have not mentioned here.)
I see your point by putting it on a tax return, it would be 'all in one place'. This is called an SA302 (tax calculation) in the UK. Even if you don't fill in a tax return, you can print off a similar document from the Government Gateway.
My advice is not to fill in an unrequired UK tax return but wait and see what supporting information the Thai Revenue Department require.