It's probably me, but I am finding your post slightly confusing.
You have originally stated Tesco broadband to Plusnet, then BT and eventually TalkTalk, then state "Both original companies claimed they'd done nothing wrong".
The way I seem to understand this, is that Tesco broadband was your original supplier and you wanted to transfer to Plusnet. Is this correct, because if so, what as BT got to do with it (other than supply the infrastructure on lease to the other two companies, which would be a private agreement between those companies)?.
Did you get a MAC code for the transfer, or any transfer dates for a changeover of both broadband and telephone?.