You wouldn’t normally remortgage property to buy a car and the bank or building society would not normally see it appropriate.
Interest rates are high a S/H car is likely to be 10% + interest and any popular small car is not going to be cheap. It depends how much you can afford, there are cheap runabouts for £2000 or less, or newer cars on finance for around £120 a month upwards but you will probably still need £2000 deposit.