NWIFlyer has answered more succinctly and effectively than what I'd written, so I'll simply add that the exact timings do matter here. Conformance is 35 minutes before scheduled departure at LHR T5, and if you haven't scanned your boarding pass at security by them you will be automatically offloaded. It's just how the system works - there is information in the App that you have to clear security by this time, and is listed elsewhere but it is perhaps one of these things that you don't know that you don't know, until it bites you

An unfortunate situation, I can only echo the advice to be as polite as possible, and to recognise the fault to be yours (even if you don't feel like it is right now) and are appealing for goodwill.

Edit: Oh and now TBS and scottishpoet have beaten me to my addition!