It was 55 minutes, but amazingly, the check-in staff at NQY were actually extremely friendly and helpful and they called the gate agents and told them to just let me on with the bag, and that if there was any trouble, they'd tag it and give it back to me at the bottom of the steps at LHR.
The gate staff were also very friendly--I do this route every week, and have never encountered anything like it---and so I was allowed to carry my bag on, and made my connection with plenty of time.
Thanks to all--this place is really a great resource.