If you can keep your house and rent it out then do it, let someone else pay off your mortgage for you
However, there are things that you will need to consider.
The first one is; can you afford to pay two mortgages if you can't rent out the original property? If no, then its a very risky business.
The second thing is; can you get a second mortgage? From a lenders point of view they will deduct the monthly mortgage payment from your income when assessing affordability. If what's left is not enough then they will decline you. However, if prove that it is self funding then it should be ok.
Also, if you don't sell your property, do you have a deposit to put down on the new property?
Legally speaking, your are supposed to inform the lender that you are renting out the property. They are within their rights to insist that you transfer to a BTL product meaning higher rates and most importantly, that you ensure that there is 25% equity in the property, if there isn't already. However, if you didn't inform them, they would never know, unless you started defaulting on the mortgage because the property was empty. Once it got to that stage, there would be no sympathy from the lender as you had breached your terms and conditions.
if you need some specific figures, just let me know