Does the Sponsoring Bank for secure collection have to be our own bank?

Does the Sponsoring Bank for secure collection have to be our own bank?

We have an agency which collects bank details for paperless direct debits,
and the collection is authorised by a sponsoring bank. The details are
subsequently downloaded and sent to a bureau which submits DDIs and
payments to BACS. Does the sponsoring bank which authorises the collection
of the details have to be the same bank which receives the payments later
claimed by the separate bureau, or could it be any bank?