Sky's migration from Google to Yahoo was done on the same day for everyone. Whilst it did result in lots of issues at the time, it did avoid a protracted migration period. Essentially they just set up the mailboxes on Yahoo, switched the MX DNS entries and migrated the mail.
They used IMAP to synchronise mail, but as a result if customers turned off a mailbox in IMAP, it didn't synchronise. Neither did the "All Mail" (label-less) email in Gmail.
It was certainly "fun" at the time, but it's now a distant memory, whilst BT's migration goes on forever. BT are also mail forwarding from Openwave servers to Yahoo for mailboxes which are not migrated, breaking SPF in the process (and has done for a couple of years now).