New height restriction barriers have been installed at both entrances to prevent Travellers from moving onto the car park in Millbrook Way.
The barriers are 2.1 metres (6.9ft) in height and some drivers say larger vehicles such as some 4x4's, vans, minibuses and motorhomes are unable to fit underneath.
There have also been complaints from drivers whose vehicles are fitted with roof racks and roof boxes, as well as those carrying bicycles or ladders.
Shock plans go in to give Preston newsagents shop a controversial new future
Evans Cycles: bike firmNN opens second Preston store to power cycling boom in city
New Preston Home Bargains opening date confirmed
Iconic Preston cafe to escape refurb of building it sits in
Preston's Fusion Trampoline Park confirms closing date for Queens Retail Park site
Ambulances and police vans are also no longer able to enter the car park but Booths say the barriers can be opened manually to allow access for the emergency services.
The introduction of the barriers has disappointed some shoppers visiting in larger vehicles, who say they no longer feel welcome at the supermarket.
"My son had to take the ladders of his Vauxhall Zafira when he went, otherwise he scraped the height bar,” said one shopper on Facebook.
Another said: “We tried to go shopping in our Transit van but we were greeted by the height restriction barriers and bollards.
"There is no way our van will get under so we had to turn around and go elsewhere. It looks like anyone driving a van or motorhome will have to shop elsewhere from now on.”
But Booths has defended the decision to install height barriers and say they are larger than those in use at other car parks.
It added that a limited number of spaces are still available to larger vehicles near the petrol station entrance, before shoppers enter the car park proper. These tend to be used for staff but will be available to anyone who cannot drive under the new barriers.
A spokesman for Booths said: “We have installed barriers to ensure parking spaces remain available for customers at all times.
“The barriers installed at Booths Penwortham are 2.1 metres, with 1.85 metres being a more common height for car parks.
“There are spaces available for taller vehicles to park at Booths Penwortham and the barrier can be opened to allow access for emergency services.”