Thanks for the reply.
It's all sorted now, and the migration is currently in progress.
I'm told that the original migration request was received, but there was a delay passing it to support to be actioned.
Maybe this is something you could take a look at? Unlike the other tickets I've raised (which were dealt with impressively quickly), the ticket for a transfer request wasn't acknowledged automatically, so I was left in the dark. It would be better if these tickets could also be acknowledged automatically, so at least you know the request has been received.
It also means my e-commerce website was unnecessarily left closed for more than 12 hours, losing income, because I didn't want people placing orders (and updating the database at my old host) while a migration was possibly in progress. I guess I should have realised something wasn't right when I didn't get an immediate acknowledgement back, so it's partly my fault for not following up sooner with a regular support ticket.
Despite this hiccup, I'm happy with the service so far, and hopeful that it will be much better than my old host, so thanks for getting it all sorted for me :-)