taurean2009:
There are a lot of issues going on here. Firstly the reason why the readings are incorrect and who took the incorrect readings and when. Secondly how often and when did a meter reader call. Thirdly, when and how was your name added to the bill.
You say EDF are being unhelful but is that in writing or just a customer service adviser's throwaway remark? While a telephone rep does speak for his/her company that doesn't mean what is said is right.
You need to get all the documentation together, previous bills in particular. It may be worthwhile making a £10 Subject Access Request to get all the previous bills, contract copies, correspondence, call logs and transcripts or recordings. You will find out what information they have. Anything they don't provide they can't rely on.
I echo maxsteam's comment that I doubt you are responsible for consumption metered before your name was added to the account.
Print out the EDF code of practice on complaints and Google for the Code of Practice for Accurate Billing (and FAQ). Go through them with a fine toothcomb looking for EDF procedural errors.
HTH