I have the exact same problem.
As a new BT broadband customer on 15 August 2018, I received the £100 BT reward card but am still waiting/chasing the £40 M&S voucher from the signing up offer.
I claimed via the online form using the AJM ref as requested and I have waited longer than the 45 days stated but still have not received any vouchers.
Why advertise these offers and then make them so difficult to claim? Can you please help me finally to sort this out now?
I have asked a moderator to provide assistance, they will post an invite on this thread.
They are the only BT employees on this forum, and are based in the UK.