But when I went that way the other day I wanted to turn right onto
Westbridge Road (the road that leads up to the heliport) but it's a
banned right turn - does anyone know if it's possible to turn right onto
Battersea Church Road ??

Yes. That's the route I use. Although the lights where you join Vicarage
Road can be a bit slow sometimes.

To get to Putney from here, I'd turn left at the first lights after you
join Yorks road, into Plough Lane. Turn right at the South Circular (can
sometimes be slow) then left at the next lights into Spencer Park/Windmill
Road/ Earlsfield Road/Penwith Road. Right at the T junction into Merton
Road then 4th left into Replingham Road. Follow this to the top of the
hill past Southfields station and turn right into Beaumont Road. This
brings you out on the A3 just before Tibbet's Corner going south, and you
can go round the roundabout and approach Putney down Putney Hill. Of
course it depends on which part of Putney you're going to and the traffic
in general, but this route is fairly free flowing.

Well the part of Putney I was going to is only really accessible from Lower
Richmond Road, so that wouldn't have been a great help, though it quite
possibly could have been if it avoided the Kings Road at the moment - I
could always have gone around the A205 and down Gipsy Lane to Queens Ride
and around that way.

Also, are all of the roads you've mentioned speed hump free?? That's one
big PITA I find in so many of the shortcut roads around South London
(particularly in the A24 corridor around Tooting/Colliers Wood).

Peter