Gym will not let me cancel and keeps taking payments

A gym cannot rely on unfair or unclear terms to keep you paying indefinitely. Under the Fair Trading Act 1986, a term in a standard form consumer contract can be declared unfair if it causes a significant imbalance in the parties' rights, is not reasonably necessary to protect the business's legitimate interests and would cause you detriment. An in-person-only cancellation rule that you cannot practically meet is the kind of term that draws scrutiny. Keep your cancellation emails as evidence, then send a final written notice stating the date you cancelled and asking for confirmation. You can also ask your bank to stop the direct debit, but do so after giving written notice. If they keep charging you, a Disputes Tribunal claim is available and the Commerce Commission can be told about the practice.