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Hello and thanks for using Just Answer.
I am Al and am happy to assist you with your enquiry.
If all your partner wishes to do is to re-mortgage the Flat, there will be no Capital Gans tax (CGT) or indeed any type of tax to pay.
CGT is only payable on any disposal of an asset, and a re-mortgage does not count as a disposal.
I hope this assists and answers your question, but please let me know if you require any further clarification.