So I'm planning this circular walk around London using the M25 orbital as a guidance and starting at Heathrow Airport. However, there's an issue towards the start of the walk where there's a footpath up to where the A40/Oxford Road up to where it meets Tatling End, and then it just disappears as you get to the A413/Amersham Road. Would it be safe to walk along the edge of this road, or would it be safer to find an alternative route?
Your question asked "would it be safe".
My answer is that yes, it would be (reasonably) safe. There are several roads like that near me where even school kids have to walk on the grass to get to their house from the bus stop as there is no footpath. The A413 has similar bus stops. One danger I find is twisting your ankle in the drainage dips that will be every hundred yards or so but hidden in the grass. That and the bottles, cans and other rubbish that has been thrown out of car windows. Of course that also might make you fall into the road.
Keep as far from the roadway as possible as the Bernoulli effect will cause the air to push you towards fast moving traffic that passes you, also the drivers are likely to not be paying too much attention when they see no footpath.
But essentially, if you keep as far away from the traffic as you would had been had there been a footpath, the only physical difference is the terrain.
I cannot say with any certainty whether it is safe. As safe as can be walking along the side of a busy road. However, you might take a look at Iain Sinclair's long and history packed walk around London in his London Orbital. Iain Sinclair didn't get knocked down walking around the orbit of London.