Well, asking a Brit this is going to get a somewhat biased answer — but I'll do my best.
Like any large group (65 million of us), we are not monolithic — some of us are right arseholes. Some of us are lovely. However, we do seem to have an instinctive politeness drilled into us at a basic level.
There is a popular myth that British people are so polite, they will apologise to you if you bump into them whilst walking on the street. So a researcher tested this — she travelled all over the world…just deliberately walking into people!
The results of this (hilarious) experiment was indeed that 80% of people in Britain will apologise to you if you walk into them. The only nation who came close was Japan, with something like 60% apologies — though she did note that the Japanese were much better at stepping out of the way and avoiding the collision! So the statistics do seem to indicate that we have a reflexive need to say “oops I'm sorry”, even when we know full well it was your fault!
For what it's worth, I would like to tell you a story, which I think might shed some more light on the matter…
Just over a year ago, I was walking out of Trinity College, Oxford — where I lived at the time. I was making my way to the supermarket to buy some milk. It was about 4 in the afternoon. About 100m from my goal, a very drunk man stumbled into me — basically knocking me over. I of course apologised to him (despite him staggering into me, whilst I was minding my own business!)
Yep. I apologised to a man, after he punched me in the face.
Now, this is mostly because my brain was about 3 seconds behind, and hadn't quite caught up with recent events — and so defaulted to “standard Brit”. But the point stands as an interesting view into how deeply the words “I'm sorry” are drilled into our national psyche!