I personally would lose the large axe and machete, add a bivi bag and groundsheet and a water filter - plus a second way of cooking. A barbie sounds great when staying put, but something that boils water fast would be handy. Plug-in travel kettle and/or some kind of gaz/petrol stove? I use a Jetboil myself - even in the car if I have to.
On a side note - it's a pity that everywhere in the UK seems to be locked down. Look, but don't touch. Kind of kills it. Reason I mention that is, I did a trip in a cheapo car through Europe last year. Motorized vagrancy I call it and I had a bloody good time. Everything from a hammock in the Italian Dolmites to sleeping on the beach in the south of France. Got some funny looks and a few questions along the way, especially coming back through Dover. But I guess they thought I wasn't worth a spin. Hope to do it all again, only this time for longer and much, much, further.
Sounds great what you're doing. Best of luck. Nice wheels for it too. 8]