Depends on the starting point, but I've always liked the walk along the Thames on the Southbank where you can meander along the restaurants and cafes there, past the Royal Festival Hall, the London Eye and then across the Westminstr Bridge to Big Ben.
Another approach is from Trafalgar Sq through the Mall and Horse guards Parade which takes you past the Churchill War Rooms. Take a left on Great George Street. An alternate route that also starts from Trafalgar Sq is to go down Whitehall, which takes you past Downing Street and right ti Big Ben. about 8 years ago