Other than speaking to a Financial Advisor/Mortgage Broker, you seem to have a few problems with this project!
1. It seems that your father relies on the rental income, but during the period of renovations there will not be any income.
2. It seems that you will have to borrow the money to finance the renovations, as your original post states that the rental on the 2nd flat will pay for the work to be done.
3. You will require a substantial deposit to put down on a new property, very few lenders give 100% mortgages nowadays.
4. No lender will give a payment holiday at the beginning of a mortgage. You will have to pay interest at a minimum, even without any capital repayments.
5. You state in a later post that you will have an income of £1000 per month, but won't this be going to your father? It may also lead to Inheritance Tax problems if, in effect, your father were to be paying your mortgage.