I would agree with The Builder that it is almost certainly a control board fault, causing the fan to run continuously.
My Potterton boiler control board has a design fault in that within a year or so of fitting, either the fan and/or pump run continuously. At resent my boiler fan is running continuously, albeit at a slow speed. It’s probably only costing me a couple of pence a day in electricity – so it is not worth fixing.
Be aware that if your BT contract does not include parts – you could be looking at well over £100 just for a control board.