This answer may change depending on the lender you used and the size of the unsecured debt you have accumulated. But yes, sometimes you can remortgage in London to incorporate your debts into your mortgage. When you do this, your monthly mortgage payments will increase, as will your mortgage term.
You should think carefully before securing other debts against your home. By adding your unsecured debts to your mortgage, which is secured on your home, you are potentially putting your home at risk if you cannot make the required repayments.
Although the total monthly cost of servicing your debt may have reduced, the total cost of repayment may still have risen as the term of your mortgage is longer than it may have taken to repay the debts originally.