"BT only allow you 50% of the top speed"
This has no basis in fact at all, i.e. dealing with support people who either
a) making it up on the basis of a false fact gets most people off the line
b) being trained very badly
There is the 15 Mbps CIR that comes with the up to 40 Mbps product, but that is ONLY a throughput guarantee on part of the network, nothing to do with connection speeds. On the up to 80 Mbps Openreach product this doubles to 30 Mbps, so (b) and a trainer with not much clue may have made some think this was the case.
The CIR is basically a guarantee that Openreach won't run the fibre backhaul hotter than these values. Again nothing to do with connection speed which remains identical no matter if the 40 or 80 Mbps product bought.
Wiring, line length, cross talk and other issues sound most likely, remember also the checker is still only giving an estimate to the DP do there is a variable length of wire to be added to that.