Can I cycle down the A3 then the A24 right from the thames out to leatherhead or is it a monster of a road with fire breathing traffic?

If not, is there a better way?

Ta

You'll be fine, joining the A24 at Clapham Common. A3 doesn't get scary till out Richmond Park way, and the A24 is like most roads out of London, so busy that it's a crawl.
EDIT: There are better/nicer/quieter routes though.

Top stuff, thanks vinnyeh

i've cycled a way that involved going along staines street into mickleham (bridleway), and involved the a217 at somepoint but i can't remember any more details…

Going to be very traffic heavy and not particularly pleasant. But do-able

Doable but unpleasant at times. Enjoy, you could be riding from Barking to Ealing on the North Circular instead.