From Chapter 1, The filling station:
The caravan was our house and our home. It was a real old gypsy wagon with big wheels and fine patterns painted all over it in yellow and red and blue. My father said it was at least one hundred and fifty years old. Many gypsy children, he said, had been born in it and had grown up within its wooden walls. With a horse to pull it, the old caravan must have wandered for thousands of miles along the roads and lanes of England. But now its wanderings were over, and because the wooden spokes in the wheels were beginning to rot, my father had propped it up underneath with bricks.
There is evidence to relate Danny to Gypsies but it isn't ever clear whether Danny himself is one. The passage above could be taken as talking of Gypsies as though from the outside - a lack of familiarity and calling the caravan an "old" gypsy caravan could imply it is no longer a gypsy caravan. On the other hand it could refer only to its age - this is clearly part of the conversation.
Poaching isn't limited to any particular group.
Edit: Slightly more definitive proof:
'Why Mrs Clipstone's?' I asked. 'What's she got to do with it?'
'Mrs Clipstone delivers everyone's pheasants,' my father said. 'Haven't I told you that?'
'No, Dad, you haven't,' I said, aghast. I was now more stunned than ever. Mrs Grace Clipstone was the wife of the Reverend Lionel Clipstone, the local vicar.
'Always choose a respectable woman to deliver your pheasants,' my father announced. 'That's correct, Charlie, isn't it?'
So clearly everyone is involved in poaching, not just a Romani community if, indeed, one is present at all. The following extract suggests Danny and his father are apart from a gypsy community.
We couldn’t afford things like that.”
“Then how did you roast your pheasants?”
“Ah,” he said.
“That was quite a trick. We used to build a fire outside the caravan and roast them on a spit, the way the gypsies do.”