There is NO legal obligation upon application of refinancing. Your legal obligation only start upon accepting & sign the Letter-of-Offer (LO).
Once you sign the LO, the new bank staff will help you liase with the appointed law firm on the refinancing matter. You have to let the law firm know the actual loan full redemption date. The law firm will help you to serve the THREE months notice to the current bank.
The law firm will call you to fix appointment for getting the paper work done.