What is the ruling on purchasing an apartment through murabaha via an Islamic bank, where the murabaha rate is variable based on the increase in real estate value, keeping in mind that conventional banks offer its purchase with fixed interest rates and allow for a reduction in the total amount upon early repayment?

The transaction conducted by the British bank is an interest-bearing loan (riba), which is impermissible in Islamic law. If the bank applies the Sharia (definition)-compliant conditions of Murabaha, which require it to first own the apartment and then sell it for a known price without any additional charges or late fees, then it is permissible to deal with it out of necessity and in the absence of an Islamic alternative.