Yes, but having other debts doesn't mean you can’t get a remortgage. The consideration is that other outstanding debts will reduce the maximum you can borrow.
Lenders look at your income, and other debts and outgoings to calculate the maximum remortgage value.
Therefore, if you can reduce other debts before applying for your mortgage, you will usually be able to apply for more.
You can also roll up the other debts within your remortgage to pay them off entirely.
As an example:
You earn £40,000 per year and pay £500 a month in credit card repayments.
Lender A lends up to four times your income and will deduct your annual credit card repayments. They can lend a maximum of £136,000.
You apply to the same lender, after having paid off that credit card debt. Therefore, your maximum mortgage is the full four times your annual salary. They can lend a maximum of £200,000.