Remortgaging - how long afterwards can you move?

King13

We have shared equity on our house with our housebuilder, interest kicks in February so we were looking to move house or remortgage before then so we can get it paid off. It's given us a headache now and put us in a catch 22 because the 20% of the house value we have to pay back puts us in a position where we have a low deposit for what we want (9% or so). Because of this so far we've been told the most we can lend is about the same as our outstanding balance on our mortgage now.
We could lend more with a few lenders but means higher monthly costs.
Partner is looking at remortgaging now to pay off the shared equity which will put us in a better position but how long roughly can you then apply to move house again? We could save lots quickly and overpay but at the moment the market by us is good and house prices are due to shoot up in the next year because of them building shops and a school. I want to move before houses get an extra 20k slapped on! Any ideas on this? Anyone moved quickly after remortgaging?