you just need to ask nicely and there are places to stop!!
seriously though, very few places to stop, and that i know of none where you could leave the boat alone appart from locking into somewhere or making a special arrangment
if you do the trip the other way round (from the sea upwards) then i reccomend overnighting at chiswick pier - 24hr access pontoon, nice restraunt / bar there too. i've done this trip a fair few times if i can be of any help just shout