Yeah I think so - as far as the lender is concerned, all they care about is how much you are borrowing and how much the house is worth. If that means you suddenly take some equity off the table, they don’t care except about the LTV bracket you’re left with.
Thanks, that's reassuring. It's my first remortgage so I'm new to this!
edit: that makes sense/seems obvious now if changing lender. Presumably if staying with the same lender they'd do something similar.