Is this a property / mortgage you currently have, or more a theoretical question?
If you already have it'll be down to your banks policy when you get to that age.
I understand it's unlikely at the moment that any of the mainstream lenders would lend for BTL beyond retirement age. You could try Dilosk or Pepper who specialise in this area. It would probably be a condition that you sell the property on retirement, or use your pension lump sum to repay the Mortgage.
If you're planning this to be your retirement fund, you should really investigate the possibility of purchasing through a pension structure if your circumstances allow it.