Gary won’t let us cut his nails either!
The only way we can get to his paws is when he’s flopping with his paws out.
We don’t touch him, just use the clippers and snip off what we can.
Fortunately, he never reacts.
As for petting, I don’t think you should force him into something he’s not comfortable with.
Some animals just don’t like being touched, and I think it’s fair enough.
To put it into perspective, if you had a friend who was extremely uncomfortable with human contact, I don’t think anyone would forcefully pull them into a hug.

I agree with YC, don’t force it. If you keep trying to let him, he’ll associate you with that action and might stop wanting to be around you. I’ve had my boys for almost a year, and it took Asriel almost 5-6 months to be ok with touching of any kind. Even now, he’s still very much not one to want pets. He’ll happily accept food from my hand, lay in my lap, but only occasionally am I allowed to pet him. He does enjoy his snoot being rubbed, but that’s mostly in his cage. When he’s out exercising, he does not want to be touched. Some bunnies are very much like that, and don’t enjoy the contact. It’s something in their personality you can’t train out of them. I think that’s such a big misconception about bunnies is that they love being cuddled and pet, and usually the opposite is true.

For nails, you can usually have the vet do it for like $15. For grooming, you can have someone hand feeding him a treat while you use a brush or a glove on him.

You only had him a month and you don’t know what his previous life was like? (I’m guessing, do correct me if I’m wrong) So for all you know he might not have been treated very well, so this could have put him off being pet. A month isn’t very long, so please don’t be disheartened I would just sit on the floor and ignore him, he’ll be curious and come up to you and then have some food on you so he associates you with something nice he’ll be won over soon enough.

We’ve had our bun for 4 months and he was straight from a breeder, he loves a head rub and shoulder rub but it has to be on the floor – he doesn’t like to be off the ground in anyway really, even if he’s sat on the sofa he’ll only be up there for 30 seconds. Part of me thinks he scared of heights

People will get fed up with me saying this as I say on all threads like this buuut….

My Peanut took months to feel comfortable with being touched. And now he’s probably the most affectionate out of him and Buttercup. Just be patient, don’t keep trying to touch him, just leave him be and soon you might ‘feel’ that reaching out to pet him will be okay. If he walks away, stop. If he doesn’t, pet him once or twice and then stop. Build up. Voila