Trust me there's a lot of people walking the streets with a lot of cash in london.
Your safe enough, as long as you don't openly make it easy.. don't leave a purse on top of an open bag, or your wallet in your back pocket, on a pub table etc. There's probably a higher risk of someone trying your inside coat jacket on the tube in a crush, but in 15 years I've never seen it happen, but the risk is there.
It's doubtful you'll end up in Tottenham or Brixton, but oppourtunists can move anywhere.
Further north in England in the towns/cities they are much smaller so the scrotes mingle closer with the normals of society, I'd be more careful at night as there's more risk of violence from drunks and theft, if your in almost any town up north on a Thursday-Saturday night after 11pm you'll see drunken brawls and smashed bottles somewhere, it's part of the culture and can happen in even quaint railway friendly places. I'd just stay away and watch, it's usually 14-20 somethings had too much and fight with a neighbour, work colleague or family member. They aren't interested in you and usually is a bit of shouting, crying or throwing up on a pavement and is over in a few minutes... just be aware it can happen like a twister from nowhere and disappear again straight after, just make sure it wasn't a ruse to get your attention whilst they grab your coat,
TBH you won't need cash though, credit cards are accepted everywhere, atm's are everywhere.
When do you fly in to the UK, I'm flying into London from San Francisco this Thursday, currently baking in the Phoenix 50+ degree oven !