Around 15 caravans pulled onto Booths car park in Berry Lane at around 8pm last night (October 22).
Police visited the supermarket yesterday evening and spoke with representatives of the traveller community and Booth's management.
It is understood that the Travellers are on their way to Holyhead, Wales, where they intend to board a ferry to Ireland for a family wedding.
It has been reported that an informal agreement was reached between the families and Booths last night, with the Travellers agreeing to vacate the car park by 9am this morning (October 23).
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But as of 12pm, all the caravans remain on the car park along with vans, cars and generators.
Barriers are down in the car park this morning and they appear to have been locked to prevent further access to the site.
No vehicles can enter or exit, meaning customers are currently unable to use the supermarket car park.
A spokesman for Booths said: "Booths are working with the local authorities to resolve the situation amicably and apologise for any shoppers having difficulty in parking.
"The store remains open as usual and there has been no disruption to shoppers."
Another large caravan has also moved onto Longridge Civic Hall car park.
One local resident said: "They have parked all across the full car park, right outside my flat.
"They’re not causing problems other than being very noisy.
"They had an agreement with Booths and the Town Council to be off by 9am, but it looks like they are clearly ignoring that agreement."
A police spokesman said: "We are aware that several members of the travelling community are currently camped on the car park of Booths supermarket in Longridge.
"Ribble Valley Borough Council and the landowners are currently liaising with those at the site to establish their intentions and when they may be planning to move on."
Ribble Valley Borough Council said the car park is privately owned and enforcement action is the responsibility of the landowner.
Longridge Town Council have been approached for comment.