Can I keep current Mortgage if Let out property?

Hi,

I've been trying to sell my property last 6 months with no luck so far and I potentially need to move for work in the next couple of months.

I have a mortgage with Nationwide that was a 5 year fix that expired last year and is now at a favourable BMR %.

I have a sizable overpayment fund on this mortgage that should be a decent deposit on a home.

My questions is:

Can I draw back my overpayment to use as a deposit on a new home and keep the existing mortgage on the old home if I let it out?

Or will the mortgage need to be changed to another product (I don't want this as it will be at a higher %)

I appreciate any comments from those in the know or have done the same.

Rick