[vinylweatherman]

Plain English?

They have accused you of being dishonest with them, plain and simple.

This could be anything from multiple account fraud to pretending to be someone you are not and using fake documents to support the deception.
To convict without trial is poor, and not something that encourages the belief that the online casino business is honest itself.
In a fair society, anyone accused of something should have the right to mount a defence to clear their name. In any case, it is quite possible that the casino/sportsbook have made an error, but are answerable to no-one.
The only resolution would be to sue Betfred for damages (defamation of character), including the disputed winnings in court (the winnings alone may not constitute a claim if gambling debt is not enforcable in law). I believe they reside in a "proper" juristiction. Look for a term stating which country's law decides the outcome of any legal dispute, and hope it is in the EU rather than somewhere like Antigua.
While you may not win, BetFred will have to justify their actions in open court and convince a Judge that they acted responsibly in coming to their eventual decision, and made every effort to clarify any perceived discrepancy to rule out the possibility of simple error rather than attempted fraud.

Even an intent to take legal action will trigger them to look again at the case, they don't want to be embarrassed in court by being criticised by the judge.
There are many examples of big companies treating customers like this, and refusing to consider the possibility that their procedures are in error. This often results in extreme embarrassment in court.
British Gas have fallen for this many times, taking customers to court for unpaid bills only for the judge to find that they are not even supplied with Gas in the first place, and why did the company not work this out for themselves when the customer repeatedly statd they had no gas coming into the property.
Security checks often fail for similar reasons. The system is fine, but it has been fed garbage instead of valid data at some point in the past. Eventually, this causes problems down the line, often for the innocent party, not the party that might have triggered the inclusion of the duff data. The innocent party really has no clue as to what the hell is going on, and as far as they are concerned they are being shafted by some dodgy operator pulling a "reserve the right for no reason" on them.