I'm sure it's hell cycling round the centre - I wouldn't dream of it, possibly with the exception of the City at weekends where it's mostly quiet, but where do you find it especially bad walking around the centre of London? It doesn't seem any worse than anywhere else to me - albeit that there's nowhere I've been in this country I'd describe as especially pedestrian friendly - and there is no shortage of routes available that avoid major roads.
One of the ways in which walking in central London is awful is the spate of new "countdown" lights for pedestrians. It's nonsense to try to tell me how long I
should take to cross the road - I need as long as I need; if my knee's playing up, and I'm carrying a load of shopping, it takes me longer (sometimes far longer than the countdown gives me). Installing these was an excuse to keep the pedestrian phase too short and give more time to traffic; it also makes many drivers even more anti-pedestrian because they think they have an excuse to try to move forward when people are still crossing and tell them "you've had your time" - it's happened to me. I know some more vulnerable pedestrians find the countdown system really intimidating. And while I'm on the topic, drivers also increasingly ignore the meaning of the flashing amber lights at some pedestrian crossings - ie the phase that means "it's still pedestrians' right of way, but if there aren't any then you can move off without waiting for the traffic's green light" - many drivers just head off and "barge through" people still trying to cross the road.
A further "subtlety" about the countdown lights which I've found alienates some people with poor eyesight is that some of them are timed with barely a second or two of green for pedestrians before the numbers start - it's easy, if you don't keep your eyes fixed on the light, to miss the green completely. And NB, thinking about the countdown, remember that the figures aren't necessarily even seconds as you might assume; some numbers change much faster than once a second.
As to "there is no shortage of routes available that avoid major roads". Well, most of my regular (quite short) journeys in central London can't do other than cross several main roads - often including the need to walk along some of them part of the way; that's how it is in central London. Not that side roads are much good very often - especially in my borough (Camden) where in my patch they seem to have a policy of moving traffic away from commercial frontages and diverting it down narrow residential streets!