I think it would be fairly unlikely that a high street bank or building society would lend you money as you have only been in UK for 4 months. Lenders normally like to know a bit more about a customer before granting a personal loan or even a credit card.
If you have a current account with a bank already, there is no harm in asking them when they would be able to consider you for a loan. You may have to be with the bank for at least 6 or 12 months for them to consider you, as well as living at your current address and having a regular job for that time too. These all help you build up points to obtain a personal loan.