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Thanks for your question - I am Sam and I am one of the UK tax experts here on just Answer.
Yes you will be liable to tax (capital gains tax) on any profit you have made on the sale of this Bulgarian property. So you need to alert HMRC as soon as the sale takes place (and this would arise even if you did not bring the money into the UK, as you have acquired British citizenship)
Then at the end of the tax year (so 05/04/2017 is you sell this property before then) you will complete a self assessment tax return to declare ALL of your income including this capital gain
You will have some exemption on any profit made as you lived here from 2002 to 2004
For information the first £11,100 of any gain will be tax free and any remaining gain will be liable at 18% or 28% or a mix of both (this is determined by your usual rate of tax and how much unused basic rate band you have.
Then any tax you owe will be paid by 31st Jan 2018 (if the sale takes place before 05/04/2017)
Let me know if I can assist further