Engagement Letter: Bookkeeper or end client?

Whilst I am comfortable in preparing and issuing engagement letters to 'normal' clients that contact my small practice directly, I now have a quick query regarding the role of the bookkeeper.

A bookkeeper (MAAT) contacted me with a view to me taking their bookkeeping data and preparing LTD Accounts, CT600 and SA100 for their client.

The bookkeeper has requested that all documentation go through her as she does not particularly want the client to be aware that she is outsourcing the year end work, and wants to add a mark-up to our fee etc.

My question is will I (ICAEW practice) still have to issue an engagement letter to the end client company, or can I instead form a contractual agreement/engagement letter with solely the bookkeeper? My initial instincts tell me that I will need to send an engagement letter (along with the normal identity checks) to the end company. Presumably, even if the engagement letter can be addressed/signed by solely the bookkeeper, identity checks on the end company would still need to be performed for ML purposes?

I am sure that this is a common occurance for many here, and am wondering what their views are?