More have since joined the group which broke into the park in Golden Valley Lane by removing a gate from its hinges.
It is understood that the group tried and failed to get on to land in Upton Cheyney before a convoy of six caravans and several vehicles drove down to Bitton where they broke into the park known as the Pound Ground.
It is believed they were a group that had previously been camping at the Lansdown Park & Ride site.
Their arrival in Bitton sparked an immediate flood of complaints from local residents to the police and South Gloucestershire Council. The park is well used by local children and is also popular with dog walkers.
A South Gloucestershire Council spokesperson said on Friday: “We are aware that a number of travellers moved on to land in Bitton late on Thursday evening. We are currently making preliminary enquiries and will be working to resolve the situation as quickly as possible.”
The travellers told the council’s travelling officer on Friday that they intended to move on to Cornwall within 36 hours.
He visited the site again today and reported that there were now eight caravans and a number of pick-ups and cars in the park. There are five families with approximately 20 children living on the site.
The traveller officer has asked the police to consider using their powers to remove the travellers as local residents say that they are being prevented from using the land, which includes a football pitch and basketball area.
Meanwhile the council has arranged for refuge bags and a rubbish collection service to try to keep the site tidy.
Travellers have also been illegally camping on open space owned by South Gloucestershire Council near homes at Siston Park.
A group which had been there for some time last month moved on, only to be replaced a few days later by more.
On Friday a South Gloucestershire Council spokesperson said the authority was “working according to our established procedures to negotiate with the families concerned to move on”.
The group left on Sunday and local residents say they have asked the council to clear the mess left behind.
Meanwhile the council says that a group of travellers who were illegally camped near Sir Bernard Lovell School in Oldland Common have now left the area.