More than 80 people have signed the document calling for the pavilion car park of Bowring District Park to be opened for those using facilities in the area.
The 30-space car park is usually used by those hiring the pavilion or changing rooms but with Covid-19 restrictions keeping these facilities closed, residents using the park, its cafe and nearby tennis courts, which are currently open, have called for a review.
Paul Kalinauckas, who started the petition, said cars lining nearby streets have made driving around the park "like dodgems".
Other residents have echoed Paul's calls, with one user raising the issue on the park's social media page and questioning the need for extra space.
They said: "I've been to the park and noticed how busy it was with cars. There were mums parked on the road pushing prams and disabled people walking with their sticks from the other side of Herbert Avenue. Does anyone know why the car park can't be opened that's situated on the other side? It seems crazy because I'm sure this would accommodate people in general but especially people with low mobility or mums with young children."
But the campaign has received opposition from nearby residents who claim opening the space would cause antisocial behaviour, and that an agreement exists to stop this from happening.
Paul, who has contacted Telford & Wrekin Council and Wellington Town Council, said he was "surprised at how controversial the issue had become" and added residents had become "feisty".
"Bowring Park is booming with visitors enjoying the facilities such as tennis, children’s play areas, football and cricket," he said.
"The park has become a place for families and social groups of all ages to meet up in the open air with plenty of space for social distancing. The café has also become extremely popular, attracting many from the local community, but the car parking arrangements are unsatisfactory. Visitors are having to park in adjacent roads when a perfectly good car park remains locked.
"Neighbours near the Herbert Avenue entrance claim a historic agreement exists to only open the car park when the changing rooms are in use but there is no evidence of this that I've seen.
"There's also a traffic diversion off Haygate Road, which is closed at one end, up to Herbert Avenue and it's like dodgems with cars parked on either side of the road.
"At the very least I would push for a review of this. If that concludes it cannot open for whatever reason than fair enough."
Telford & Wrekin Council has been contacted for comment.
The petition can be viewed at petitiononline.uk/open_bowring_park_changing_rooms_car_park