In reply to FesteringSore:
When did you open the new card account? That's when the 42-month interest-free period starts, not when you transfer the money.
It'll cost you £59.80 to get a £2,000 balance transferred. As I said above, I
think you need to clear that from the new card before the first minimum payment comes due, otherwise you will get charged interest on it. But don't take that from me, call the card company to check.
Do you know what the minimum payment is on the new card? It's usually a small percentage of the outstanding balance, so it will go down over time as the outstanding balance won't (shouldn't) be accruing interest. It's highly unlikely that paying the minimum over 42 months will pay off the full amount, so you need a plan to pay off what's left at the end of the interest-free period.
Re-reading your OP, it's not clear to me whether you will get deal A) or deal B). I would urgently clarify which one you are on/will get. Deal A) is vastly better than deal B).
Post edited at 15:04