When you remortgage you're not buying a new home.
It's about switching your mortgage to another mortgage lender, in order to lower the amount you're paying on your mortgage.
In short a remortgage is about saving money.
It is of particular relevance if the value of your home has risen.
Remortgaging usually involves changing your mortgage lender, though not necessarily.
Most lenders offer the sort of special deals you'll be looking for only to attract new customers into their web and deliberately exclude existing customers. However you may find that your lender offers you a better deal so as not to lose you. (This would still be remortgaging).