if you hand the keys back how would you enter the property???
If you wish to delay leaving the property then clearly you should not hand the keys back but rather stop paying the mortgage. This will lead the lender to follow the process of repossession and eventual eviction which is likely to take a minimum 6 months from the first missed mortgage payment.
You should only surrender the keys voluntarily if you intend to vacate the property voluntarily. John White England Jackman & Spacey