just done this.
If you want the best deal, you'll shop around. If ypou move lenders, they will revalue and your LTV will change. I say change as there aren't always guarantees, and you may win/lose.
When your LTV falls into a new threshold (85%/80%/75%) you get different deals, and can save money (we kept our repayments the same, but lopped a year off the mortgage.
Factor in £750 + any mortgage fee's (and if it says a feew is at completion, that means when the mortgage is in your name, not when you pay it off).