The rules when you re-mortgage are the same as for a new mortgage. Monthly costs will vary depending on the type of mortgage you take out, the outstanding balance from your previous mortgage and the term over which you make the new borrowing.
If you re-mortgage over a longer term you will reduce monthly costs, but it will take longer before your home is really 'yours'. Your lender may also charge you for leaving your current deal, which will eat into any long-term savings.
If you are looking for an online mortgage UK lenders should provide full details of their products on their website.