River route from Charing Cross to Hammersmith?

You can't go all the way. You have to kind of cut through Fulham once you get to Cheyne Walk.

Sadly this is true. I've been hunting for a riverside route back from Westie drinks for ages. Still not found one.

South Bank is better (at least to Vauxhall Cross) from the West End, apart from the bit by the Eye, but you can go on the freshly tarmaced bit round the back of the hospital.

EDIT, thanks to Mashton, I think i've found one.