Looks very pleasant Smojo.
Not sure how TPO's work in relation to your wood, it must allow for sensible forestry rather than 'thou shall not remove a twig'. I'd hope it permits a degree of thinning and encouraging biodiversity, thats just good practice.
As Dexter said, there'll be lots of advice but don't forget its now yours and its ultimately up to you what you want to do.
I started with aspirations of doing everything by hand, and have the bramble wounds to prove it, but I think in about 6 hours of brushcutting I cleared as much as took 6 months by hand. Love my Husky, but its currently rested until after the birds have finished nesting.
The FC and a private consultant, both of whom were pretty eco-aware both advised over aggressive brambles should be ruthlessly hacked back and either roots pulled up or treated with SBK to stop them coming back. Some are OK, but you can have too much of a good thing. Looking at the diversity and vigour of what we have regenerating I feel fully vindicated in the (minority) I've so far removed. I like the fruit, feeding butterflies and birds associated with bramble, but whats replacing them will be better and more diverse. We had 60% of the wood inaccessible from brambles and I've now cleared a quarter of them, its looking good and I'll do a post showing the regeneration, in season 2 it gets quite exciting.