Is it permissible to obtain mortgage (loan) in UK for buying a house on interest. Please send me an answer in detail with Islamic arguments

Yes, this is permissible in Islamic law. This is because it is considered a form of Murabaha.

Murabaha is a sale in which it is permissible to stipulate an increase in price in exchange for deferring payment.

Even though deferment is not considered real currency, in murabaha, there is an increase in price for deferment. The objective is to conclude the sale when there is an agreement between the two parties, there is no objection to the sale and people, buyers and sellers, are in need of it.

This form of transaction is not considered riba [usury] according to the legal maxim:

When the commodity comes between two transactions, there is no riba.
God Almighty knows best. Mortgage takes the same ruling as a commodity.