Although the various responses to OP's posts have fairly informatively set out the policies and procedures at T5, I do think there's a whiff of "computer says no" about those policies, and not much sympathy has been expressed for the way OP was treated. It really does sound as if BA doesn't really give a t*ss about passengers who find themselves in OP's situation.

By way of contrast, the last time I missed a connection it was in December when my Qantas flight from EZE to SYD arrived half an hour late so I missed the last flight to AKL. Qantas did the following (without in any case my asking for help or information first):

1. The reason for the delay (baggage handling system computer failure) was announced - and so I knew it was not Qantas's fault;

2. Lead FA in my cabin came to me before take-off to say they were aware of my connection and would provide information during the flight as to what would happen once they knew just how late they were going to be;

3. CSD came to me a couple of hours into the flight to explain why they would be unable to make up more than half the delay to the flight in air;

4. CSD came up a few hours later to confirm I would miss the connection but I had been re-booked and a Qantas rep. would meet me on arrival;

5. The Captain came down from the cock-pit to apologise personally for the missed connection! I said it's not your fault but I appreciate the gesture.

6. On arrival there was a Qantas rep. who handed me a revised itinerary, details of my hotel and two taxi authorisations to get there and back.

7. He came with me to immigration and took me through the Australian citizens area to avoid the queue for non-residents. "Don't worry, you're with Qantas" he said when I asked if that was o.k. given my UK citizenship.

8. The Qantas guy waited with me until my bag appeared, then gave me a card with his mobile and a customer services number saying I could call with any concerns I had. He asked me if I was happy with the crack of dawn flight I'd been re-booked onto, or whether I would prefer to have a lie in and wait for a later flight. He said I had specifically been re-booked into the same seat I was supposed to have had on the missed flight but if I wanted to change he would arrange it.

9. After confirming that any taxi at the airport would accept my Qantas vouchers he asked if I needed anything else and left me when I thanked him but said no.

I would suggest there was a thousand light years difference between the service I got from Qantas and the service OP got from BA, and just saying "that's the system" isn't an adequate answer IMHO. My favourite airline could and should do better!