Yes, you could remortgage the flat and use the money towards another house. There will be tax implications on the flat when you do an annual return i.e. the interest on the mortgage payments wont be allowable against your tax bill, so you might find yourself paying more tax.
Although it sounds like you might get a good yield on renting the flat, do allow for voids (periods in between tenants when you wont get any rent) plus other costs, repairs etc. And, if you use an agent they'll take a cut too.