Thanks both, yes, the problem is extremely short time, I think I won't make it if I have to go all the way out to the Tube/Heathrow Express. I'll do my best to convince the Flybe gate agent that it'd be really nice of them to let me take my bag on, as I've paid for it anyway and it won't earn them any extra revenue. I have pictures of it on their Dash-8, sitting nicely even under the hinge of the bin, but I imagine they'll say `computer says no'.
So I guess I'll probably miss my connection, but fortunately it was a short and inexpensive positioning flight and I'll have time to get another in the morning in the worst case. I was hoping Flybe would have rebranded and ditched this policy by now, but I should have guessed their rebranding would have about the same on-time performance as everything else they do...
Thanks again to both of you, at least I won't be wondering about this the whole way up tomorrow.