Normally, the money will be banked into your desinated account within 2 weeks time after the original mortgage switched to the new bank.
For paid up property, normally it is faster, as there is no need to serve 3 months notice.
For property with outstanding mortgage, the shortest time line is about 3.5 months from the date of accepting Letter-of-Offer (LO), as the current bank always requires you to serve 3 months notice, regardless within or out of lock-in period.
You can further shorten the notice servicing period by paying pro-rated 3 months interest to the existing bank and ask the law firm to expedite the process for you. The expected time line for this route is approximate 1~1.5months.