I, like yourself, had to borrow from the folks to make up the deposit and stamp duty. It never came up at the bank (other than for them (my folks) to sign a letter stating that they don't have any interest in the house, despite their having put up some of the purchase price) as by the time I had drawn down the mortgage, I had already paid the deposit to my solicitor upon signing the contract to buy the house.
You should be able to get approval in principle (I say "should" as the last time I took out a mortgage was before the crisis) for a percentage of the house price, and your word that you've got the deposit sorted should be enough.