Interesting OP. I have spent a lot of time in both London and Paris for work. I have rarely felt threatened anywhere in the UK. Last time I was London, I stayed in Kensington, a pretty upper scale neighborhood and I saw dozens of cops walking around the high street, carrying MP5s. Also saw plenty of MP5 toting cops near Big Ben and at #10 Downing Street. We did a two week trip last year to England and stayed five days in London, hung out with 40k stoned freaks to watch Summer Solstice at Stonehenge, then rented a car and did a trip through Salisbury, Bath and the Cotswolds. Did not feel any real threats anywhere. Most of the areas we were in were pretty touristy, had a wonderful time.
Paris, been there five times. I am a photographer/cinematographer and am often toting around lots of expensive camera gear out in the open, shooting at night, by myself. One time, I was on the Metro, riding with my wife, carrying a steel tripod and I could tell that a guy sitting across from us was sizing us up for a pickpocket, or grab and run, I could just tell by how he was eyeing us, I had my camera bag and tripod. When we got up to disembark the Metro, I began waving my relative heavy steel tripod around casually, remarking out loud, in French, "Wow, I bet getting your skull crushed by this would be pretty painful" to my wife. I also made direct eye contact with the guy. He took off. That's the only time in Paris that felt sketchy. We rented a car and drove down to Grasse, Eze, Nice. On the way, we were in a crowd in Aix en Provence, standing in line to get some lunch when a girl pick pocketed a tourist's purse, just snatched it and ran. I made chase but she was faster than I was and had a head start. The woman who had her purse snatched was screaming, it was crazy. On the same trip, we stayed in Cannes and were riding a public bus. My wife and I were the only ones on the bus who were not Muslim and my wife's exposed legs were drawing death stares from a lot of people. France is more Muslim than not now, they gave away their country.
I agree with the others, situational awareness is number one. Not looking like or acting like a tourist would be number two. Anytime I travel to a non-industrialized country, I research and hire a "fixer" whose job is to make sure that we are not hassled, shaken down or kidnapped. I get references from known sources and have had very good fixers all over the world. I don't do that in industrialized countries, but in Morocco, India, Vietnam, anywhere like that, any African or Muslim country especially, just hire a fixer, they can keep you out of trouble and make it so you don't get into trouble, well worth the cost. Out fixer in Morocco saved our butts big time this past May. We did a work expedition out to the Sahara and on the way back, I had a Go Pro on the hood of our van to shoot time lapse video of the road trip and scenery. Coming back from the desert, into the town we were staying in, we were stopped by a couple of cops at a roadside checkpoint. Our fixer spoke them in Arabic and it started getting pretty heated. Turned out I had accidentally shot time lapse video of them coming into the checkpoint. Moroccan police do not like being on video, at all. Our fixer smoothed it over (he knew one of the cops) and he told me to delete the footage, which I did. But think of what could have happened if we wouldn't have had our fixer. Get it? I had no idea there even was a checkpoint coming back into the city so it was my bad, but thank goodness for our fixer.