Tax relief on interest paid is available on business loans, or loans to buy property for renting out. Although the terms and interest rates for such ‘business-related’ loans may be different from a domestic mortgage, the tax relief for a top rate taxpayer can reduce the cost to half of what it would otherwise be. If you achieve 50% tax relief on interest paid at 8%, this is less than paying 100% of interest paid at 6%! If the rates and terms are the same for two loans, tax relief is a pure advantage.
If you are going to pay down your borrowings, look at the net cost after tax relief rather than the gross. You might want to reduce ‘private’ borrowings, even if the interest rate is lower, before you pay off loans on which you get tax relief.