I haven't just told you what the HMRC site says - I have advised you how your UK tax position would be if you became resident again in the UK - which is what you had asked for ! (You stated I'm British, 70, based in Mauritania, live half-time in the UK, non-resident so far. I have one rental flat in Spain, one in Paris, one in UK let ehen I'm away. Both flats abroad pay 20 percent tax. What eould the incidence be on my UK income tax if I become resident?)
BY offset I mean say with all your incomes HMRC stated you owed £2000 but you had suffered £1500 (when converted to sterling) in French and Spanish tax - then the foreign tax deducted from the UK tax would man you would only have £500 to pay (in this example) but if the foreign income you had already paid was more than £2000 the UK tax office (HMRC) could not refund you anything back.
I don't know what the offset will be - you would know this as you advised me that you paid foreign tax on the rents already when you stated "Both flats abroad pay 20 percent tax"
But from an initial UK position if your income was 24K plus £10 K rents (not sure what the figures 15K plus 13K Euos are relevant to) this would be an annual income of £34,000 from which the first £11,500 would be tax free leaving £22500 at 20% = £4500 UK tax due -
So any foreign tax paid, you would you declare at the same time as the foreign rental income (On a self assessment tax return for the UK tax office) and this would be used to reduce the tax bill of £4500