The only place I've ever worn a money belt was in a developing country - one of the rougher areas of Guatemala City - I've never worn one in the UK, nor when travelling in Europe.
Of course, every city will have pickpockets, but even in places like Central London, where the authorities warn you to to be extra careful with your belongings, the most I've ever done is hold my purse tightly to my side, with my hand firmly over the zip as I walk through the streets.
Really, one of the main things you have to be careful about is withdrawing money from an ATM, because it's not hard for people to look over your shoulder to see your PIN number - as long as you shield the keypad from view when using the ATM, you should be fine.