AOL BB's parent co. is TT but AOL BB operates its network separately from TT, probably due to conditions imposed when AOL UK (part of AOL Inc) sold its UK BB to TT.
AOL BB does not offer FTTC, tho' I see no reason why you shouldn't be able to migrate to TT. Are you still within your min. contract period with AOL BB? Maybe that's why she said it couldn't be done (without incurring cancellation fees).
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 19 Meg WBC