McNally told BBC Radio 4’s Today programme that the village could also apply the new Hillsborough Law.
Once passed, the law would create a legally enforceable duty of candour which compels public officials and authorities to act transparently when investigations and inquiries take place.
McNally told the programme: “Last night, [Prime Minister] Andy Burnham was on a podium talking about the violence, sexual violence towards women, and bringing it upon the media industry as their responsibility to manage.
“But the reality is, is that this is exactly what the government is doing to us here.”
Asked how the village would respond, he said: “There’s going to be many actions, you will see. We will disclose that as we move forward.
“Today is a day of reflection, and we’ll work out where we plan to go from this point. But I will say, the Hillsborough Law is there for a reason, and we’re going to apply it.”
Asked if ministers should be braced for a legal challenge, he said: “Absolutely, absolutely.”
Piddington symbolically voted to leave the UK in September over the planned use for the site, and last month the group Wrong Plan Wrong Site appealed for a judicial review into the proposals.
A government report said the decision received 3,177 representations against and one in support.
It also said Rayner had ruled permission via an Urgent Crown Development application should be granted because “national demand for asylum accommodation remains high”.
The permission allows for demolition of existing buildings, the building of new modular accommodation, and provisions for health and welfare facilities.