Balance Transfer B*lls Up!!

Late last October, following Martin's advice he gave on a tv prog, I applied online for a well-known credit card to take advantage of their generous interest-free period. I transferred the balance from an existing card but, despite the sum showing up on my new card account, the sum owed on my old card showed no change.
I contacted my new card's issuer and after several days it transpired that money had been transfered to my new card from someone else's credit card account. My new issuer claimed that I must have made a mistake in entering my old card number but said the mistake would take about five weeks to fix.
Here we are in 2018 and, despite several calls to the new card issuer, they still haven't been able to return the money to its rightful 'owner'. During the last call from them, on Jan 9th, their rep offered me £10 as a token of goodwill but told me he couldn't authorise the mistakenly transferred money to be returned but would have to pass it over to another department. It might take five weeks to rectify the error, he said.
I've heard nothing more since then.
Surely, if I had made a mistake entering my old card's number they could, by checking it against the correct number, spot the error and return the transfer? I do not believe that it was me who made the error but it was a mis-type by one of their employees. They also asked me to give them the expiry date of the old card and its security number in order that they could return the money. My old card issuer told me that this extra information is totally unnecessary when correcting a transfer mistake and they, like me, were suspicious as to who had actually made the error.
Thankfully, no interest is acruing on my new card account at present but what do I do now? Contact the banking ombudsman? I'm at my wits end with my new card issuer and am sure they are fobbing me off with excuses.