2009 Specialized Rockhopper Comp Disc, 2009 Specialized Tricross Sport
What kind of bike do you have? Depending on exactly where in London you're starting from and whether you want a head-down-and-blast-it route or a more scenic route you could consider following National Cycle Route 4, which goes through Richmond Park, along the Thames past Kingston and Hampton Court, then on to Walton-on-Thames. NCR4 will turn a 30 mile journey into a much longer trip but will be more scenic.
I've only cycled a very short length of the A4 around the Hounslow area and didn't enjoy it much. I also cycled a very short (about half a mile) length of the A316 about 2 miles before it became the M3 and have never been so glad to turn off a road in my life. That said if you've got a racing bike and you're faster than me on my mountain bike you might feel more confident.
Have a look at bikeroutetoaster.com for some route ideas, and use Google Maps with satellite and street views to get a feel for what sort of traffic volumes you might encounter and how wide the road is, if there are specific areas that concern you.