Is it Islamically permissible to purchase a house in Britain through Sharia-compliant mortgage bonds from an Islamic bank, where the bank pays 80% and I pay 20%, then I make monthly installments that include repayment of the bank's share and rent for my occupancy of its property, with the rental terms reviewed every six months until the full value of the bank's share is repaid?

It appears from the question that the bank sells its share of the house to the buyer in installments, retaining ownership until the full payment of installments. During this period, the bank leases its share to the buyer. This type of transaction, known as "Ijarah Muntahia Bittamleek" (lease-to-own), is impermissible for reasons including:

1. Violation of the sale contract, as the ownership of the sold item does not transfer to the buyer, whereas the essence of sale is the transfer of the item to the buyer. 2. Combining two contracts (sale and lease) on a single item at the same time, even though they are distinct contracts with different rulings.

The Sharia-compliant solution is for the bank to sell its share of the house to the buyer in installments, and make the house a pledge (collateral) to guarantee its right.