The supplier has to have a code of practice or customer charter or some such thing, and I believe one of the things these should include is an obligation on them to visit and read meters at least once a year. The Ofgem website may also help with info. on the supplier's obligations.
Look at their website and see if you can download their charter, or ask them to send a copy. Then you can go through their formal complaints procedure and - if not satisfied - go to the Energy Supply Ombudsman (see website) if the supplier is a member of that scheme.
If you do have to pay anything, you should not accept what they say about the speed of payment - they should be willing to accept a payment rate that you can reasonably afford.
If necessary, get help from your local CAB to deal with them.