Travellers are said to have abused and intimidated leisure centre staff and councillors as they tried to get onto land.

At one point, the group are claimed to have stopped customers of Splashes from leaving the site, as workers at the Rainham site attempted to block their entry.

A separate group, who left the Riverside Country Park earlier this week, has now arrived at the Tesco Extra car park in Gillingham.

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The group moved into the supermarket car park during the afternoon while another group of travellers set up home on another green space managed by Medway Council, Cozenton Park in Rainham.

It is understood staff at the store were forced to close the car park at one point as reports customers’ cars were being damaged by young individuals running around with trolleys.

The store, which is usually open 24 hours also had to be closed for a time during the night for safety reasons.

VIDEO: Travellers pitched up in Rainham

A spokesman for Tesco, said: “Unfortunately, due to an incident of anti-social behaviour, we had to temporarily close our Gillingham Extra store last night.

"We are assisting the police with their enquiries. We are sorry for any inconvenience caused to our customers.”

A fence post had been broken down at the Splashes Leisure Centre car park, enabling vehicles and their caravans to enter Cozenton Park, in Bloors Lane.

The police were called out to the park and one patrol car was parked across the gap to prevent an further vehicles from entering the area.

Ward Cllr Martin Potter, (Con), went to the scene when he heard about the invasion.

He said: “I arrived on the scene at Cozenton Park and parked my car in the breach area to prevent further incursions, however, as they were leaving, the police asked me to move my vehicle and stated that it could be damaged if I didn’t.

“Just prior to the police departure, children from the skate park reported an incident with a scooter being thrown at them.

“I asked for officers to immediately investigate this and they did."

Cllr Potter also said some of the men from the group approached him and Cllr David Carr and asked what was going on and both councillors were then subjected to a barrage of abuse by the group, who also threatened to “mess up the place” if eviction action was stated.

The Splashes car park gate was also closed for half an hour to prevent any more travellers arriving on the site.

Cllr Potter added: “Some of the traveller group had gone out and demanded access to the car park on their return (to get their vehicles into the park).

“The brilliant staff at Splashes explained to the travellers that they could park on the highway and access the park on foot, but this was not accepted by the group.

“The traveller group then abused staff, threatened criminal damage and attempted to intimidate staff.

“The staff stayed calm and reiterated that the car park was closed to incoming traffic to avoid disruption to the leisure centre and that it is always locked overnight.”

It was at this point some of the group then blockaded the gate and prevented customers' cars from leaving.

Cllr Potter added: “This was followed by more abuse and attempts to intimidate staff.

“The staff locked the Splashes doors, called the police and reassured customers.

“They handed out water and did a brilliant job of remaining calm whilst also keeping everyone else calm.

“The traveller group eventually gave up on their blockade and drove their vehicles across the mound in front of Splashes to access the car park and then onto the park.”

When police arrived shortly afterwards they advised the group the gate would be locked overnight.

Cllr Potter added: “This group of travellers have proven to be particularly threatening and abusive, and I must commend the brilliant staff at Splashes for the valiant professionalism I witnessed in light of such adversity.

“Furthermore, efforts are underway to evict this group and all these recent events serve as a reminder of why we need a change of law to deter these illegal encampments.”

A lot of rubbish was left at Riverside Country Park, in Lower Rainham Road.

Some of the travellers were still at the Tesco site earlier this morning, but have now moved and set camp at the Greenfields boot fair site in Wainscott.

A Medway Council spokesman said: “We were informed that a group of travellers had set up an illegal encampment in Cozenton Park on Thursday evening.

"It is thought some of the group accessed the park through Splashes car park. The police were contacted after vehicles were used to block the entrance to Splashes car park, preventing some of our customers from leaving the centre.

“We will continue to work closely with the police to monitor the situation and will be following a civil legal process to move them on if they remain on site.

“Splashes leisure centre is open as normal and, as a precaution, we have arranged for security officers to visit the area over the weekend to help prevent any incidents of anti-social behaviour.”