They expect us to wear high vis jackets at work occasionally (mainly when we go out onto the forecourt) but they make you sweat like a bitch, additionally a training DVD we've been made to watch have omitted to mention this rule - by showing someone go out to the forecourt on many occasions without a high vis vest. There are other things which I have decided to ignore. But it's a good thing to rely on if I get run over.
EDIT: Wouldn't bother with high vis jackets if a light does the job. I don't use a light when I use my bike. If a driver can perform an emergency stop on the presumption a child/whatever has just crossed their path, I assume they can accomodate for seeing a bike (at least) five metres away.
As for the backpack, the solution is obvious: if you need one - use it. Depending on the content you may sweat a bit, but as you said you'll be wearing some non-work clothes. So shouldn't be a problem.
One thing which has intrigued me, is it only in London where you can get a quote on a bicycle and possibly haggle? It's not exactly an insurance quote.