You might find
@Solocle's LEJOG writeup at
https://www.cyclechat.net/threads/lejog-august-september-2021.278993/ interesting. Obviously he was heading north rather than to London but the route through Cornwall/Devon will still be relevant. Personally that sort of road gives me the heebie-jeebies but each to their own!
Surprised this needs to be asked. The fastest roads will be A30, A303, A30. Nothing has changed about that in decades. Whether you’d want to be on them is another question. Personally I wouldn’t touch them apart from in middle of the night when it’s quiet. During the day you’d want a follow car with a big fook off cyclist ahead signs on it.
Unfortunately the sort of distance where it can't be organised to be all at night.
It's worth noting that, other than LEJOG, I've also conveniently done the route down from
that London.
Timings depend hugely on what sort of speed you're travelling.
I'm quite proud to say that I've cycled the entire length of the A30 between London and Honiton at some point or another. Well, Westbound.
As for the entire road, my LEJOG was obviously eastbound, so that screws over the timings a bit.
Anyway, Cornwall is the real problem. The big detour I made was A39-A395. I did do the A30 West of Hayle, and between Chiverton and Carland Cross, plus a short dualled bit. This was OK, if rather grotty.
The few miles on the A30 approaching Launceston were fine, as it was 2am and virtually deserted.
Once you get past Launceston there's the old A30 all the way, bar a couple hundred metres at Sourton Down. Actually I got carried away with the downhill there and did the whole Okehampton bypass.
My recommendation would then be to take the A30 from Honiton. Well, there's a nice little back road for the uphill bit, which reduces the time for the trunk road bit to a couple of hundred metres, rather than several kilometres slogging up a hill! I went the A303 route on LEJOG, but that was because it's 200m less climbing. The A30 is more pleasant here, for sure, and simpler to navigate, which wasn't so important for me.
Basically just follow the A30, it's fast, and generally a reasonable route around these parts.
Now to follow the A30 you have to do a couple of miles on the A303, or a decently sized detour. My London ride was heading the other direction, so I hit this point at 2am, whereas you might want to be earlier than that. Actually I did 30 miles along the A303, because I fancied Sunrise at Stonehenge... But just follow the A30.
This takes you straight to London.
If you make really good pace you could wangle it so that it's late when you're having to do the A30 in Cornwall, you do the A30 through Dorset in the daytime, and then it's night again as you do the last bit into London! But that's awfully optimistic for 500 km, at least for me.
Once you get there the A4 takes you straight into Central London, I followed the A315, Roman Road.