My perspective as a traveller is that London and Paris have no greater level of violent thefts than any other major city but those who have honed the dying art of pickpocketing are still more prevalent in European cities, especially London, Paris, Venice and Lisbon.
My advice is - be alert. Don’t be a walking advertisement of wealth, don’t be an easy target (distracted, open purse, leave it on a counter etc) and don’t take anything you cannot afford to lose.
At the end of the day, you will likely stand out as a tourist and, as you are focused on the sites, someone might take advantage. The only thing that says about London is that there is so much to see.