I think that the key question here is not what time you set foot in the check-in area, but what time you reached a check-in desk and started to talk to an agent there. And had you used an SSCI machine to check yourself in before approaching a desk?

If you presented yourself for travel in time, and were then denied check-in (and therefore boarding), then I think that (a) you have a valid complaint to BA; and (b) you may possibly have rights under the EU Regulation (for the reading of which I recommend the prior application of a cold wet towel to your forehead).

But if you didn't use an SSCI machine and you didn't reach a desk until after the -45 minute cut-off time, then unfortunately you were simply late for your flight.