The petition was set up online by James Brand, who explained his personal reasons for wanting to improve provision in the town.
“As a parent, who has lived in Whitehill for seven years, I find it disgusting that if my young family need medical attention we would need to travel up to an hour to the nearest Accident and Emergency (A&E).
“With all the houses being built in the area and the growing population, there should be a 24-hour A&E hospital for the residents of Whitehill, Bordon, Lindford, Headley and the surrounding rural villages.
“Currently, the nearest A&E is either Guildford or Basingstoke, both of which are up to an hour away by road and, given the increasing population, those existing A&Es will not be able to cope with the influx of people using the services.”
He added that his pregnant wife had to travel to Basingstoke for an emergency ultrasound scan as there was not one available at Chase Hospital in Bordon.
Mr Brand has received support from Whitehill and Bordon Community Party, which he has joined and become its health spokesman.
Party leader Cllr Andy Tree said: “I appreciate the pressures that the NHS are under, but it would not be fair to short-change the people of Whitehill and Bordon.”