However, the Duke and Duchess of Cambridge, along with the Duke of Edinburgh are patrons of the club.
Kate, who is known for being sporty, is said to often visit the club with her children and friends.
The new rules could mean her staff are at risk of being fined if they drive through the vicinity.
Other members of the club shared their horror at the “preposterous” new rules.
One member said: “If this scheme goes ahead it could mean the club has to log all royal number plates and send them to the council to prevent the Cambridges and their staff being fined £130.
“It’s absolutely preposterous. It going to cause all sort of mayhem.
“It is also a disgrace, as the permit signs are so hidden on the roads, I know of members who have received a fine without knowing why.
“I think Kate and William will just stop coming — they won’t want to give their number plates to the local council.
“There is also a security issue as well.
“It is outrageous they have to let council officials know in advance when they are coming or risk getting a £130 fine.
“And it is not just their car, but their nanny and their security officers.
“There are always at least two cars when they come.”
However, the council has said the Duchess will “always be welcome” despite the potential fines.
A spokesperson for the council told the Daily Mail: “The Duke and Duchess of Cambridge are always welcome in H&F.
“Free access by road to the Hurlingham Club will continue as part of the environmental measures we are considering.”
Prince Philip also is a fan of the club.
But he may not be affected by the new rules.
This is because he usually arrives by helicopter instead of a car.
A member added: “We always know when he is coming as they mow the lawn.”
Source: EXPRESS CO UK