We just have an Australian style offset mortgage. A standard repayment mortgage but with paired savings and current accounts. Any money in the savings or current accounts means you don’t pay any interest on the same amount in the mortgage (your mortgage principal is temporarily reduced, so you pay less interest as the principal is smaller). The cost of this is no interest on your savings, but in almost all savings accounts this would be a lower rate than mortgage rates (as bank profits are based on this difference), it is a net win for you.
We now have more money in our savings than is left on the mortgage, so we pay no interest, just the principal. We don’t pay off the mortgage as we have the flexibility, the liquidity, if we need the money in an emergency.