They are on a shortlist of possible locations for a 1,700-space car park and railway station as part of the controversial HS2 rail link.
Users of the planned £55bn rail scheme would park at the new site to board trains to join HS2 at Sheffield or Leeds.
Jon Trickett, the Hemsworth MP, accused the government of keeping the park-and-ride plan secret after it was leaked last week.
He said: “These plans have been kept secret intentionally.
“We were meant to be kept informed by the Department for Transport, but they’ve had no contact with me or my office.
“Equally importantly we have no idea how the narrow roads and lanes around either Fitzwilliam or Hemsworth would cope with possibly thousands of car movements per day.”
Last Monday more than 170 people were at a public meeting called in opposition to HS2, which opponents say is waste of money which would carve up the district’s towns, village and countryside.
Wakefield Council leader Peter Box was among speakers at a packed community centre in Altofts.
Paul Dainton, who organised the meeting at The Brig, on St Mary’s Road, said: “It’s going to go through our green areas with the destruction of woods, water ponds, wildlife areas.
“It will lead to the loss of 22 public footpaths in our wildlife spaces. It’s going to be more than the width of a football field. People are not interested about what the HS2 route should be, they simply don’t want it, full stop.
“The disturbance while it is being built will be horrendous.”
Mr Dainton said there were concerns about the rail line running across land with subsistence caused by disused mines. People were also worried about losing thousands of pounds off the value of their houses.
Mr Dainton added: “The compensation offered is appalling considering what will happen to house prices.”
Mr Dainton urged people to take part in a public consultation on HS2.
Existing Wakefield-London trains could also be reduced if new HS2 trains from Leeds to the capital are introduced under HS2, it is also feared.
HS2 campaigner Robert Burgess, of Altofs, said: “More than 170 people turned out on a cold winter night to attend the public meeting on Monday night.
“These people showed their support, accepting that we could not just lie down and let this government push on with what most people from all sectors have named ‘a great white elephant’.”