By the letter - none, although you would be entitled to a refund of any taxes and fees (e.g. airport and departure charges) because you didn't use the ticket.

Unfortunately, and I'd have hoped the check-in agent would have advised you to hurry, you missed conformance. From landside to airside (i.e. not transfer security) that's pretty black and white unless you're a very frequent traveller, probably departing from a nearby gate, and only having hand luggage - and even then a call has to be made to the gate to see if they'll accept you.

It's possible, of course, that you (or rather your baggage being unloaded again) caused the 35 minute delay - very difficult to know if it could have reached the aircraft in the 10 minutes it took for you to reach security after checking in.

In practical terms - if the check-in agent didn't alert you to the possible issue, or if the queues for security were impossibly long, you could try and get rebooked for later in the day (it's not clear if you're still at LHR) by asking very, very nicely at a customer services desk.

You were cutting things incredibly tight though, so you may find sympathy from BA in short supply - arriving with a checked bag right on the drop-off deadline and expecting to make it through the system would be way beyond the risk appetite for most people here.

If you need to travel now, you should probably expect to be reaching for your wallet, and accepting anything better is a bonus.