Doubts

I personally wouldn't ride fixed with a significant amount of weight, esp panniers. I'm not surprised you came off, it sounds like it was inevitable. And in the long run not good for your knees.

That's strangely reassuring! I wonder what counts as a significant amount of weight - I will always be carrying a laptop, papers and a change of clothes - but maybe that's not very heavy. Sometimes it'll be more.

You could go singlespeed with a slightly relaxed geomentry (maybe a path frame?) which'll help you balance the weight.

What's a path frame?

But for town riding, fixed with a tight frame is best - you'll get the agility you need amongst the traffic.

Presumably you don't commute from the cotswolds, so have you thought about 2 bikes?

I live in Hampshire - the commute is 5 miles to the railway station, then a journey into London, then on from Waterloo.

2 bikes is a good idea in the long run, but for now the budget is fixed at about £500 - so it's a case of which to get first.