Just 124,394 new cars were registered last month, the Society of Motor Manufacturers and Traders said.
That was down 20.6 per cent compared with the same month last year.
Jaguar Land Rover, which has its engine manufacturing centre at the i54 north of Wolverhampton, saw bigger percentage drops in sales of its vehicles.
Jaguar was down 53.3 per cent to 1,102 cars with Land Rover dropping 33.8 per cent to 3,635.
Longbridge-based MG was one of the few car makers to see a rise. It was up 28.1 per cent to 3.143 Its cars are designed in the UK and made overseas.
Ford topped car sales for the month with 11,106 – down 2.8 per cent– followed by Volkswagen with 10,502.
Overall it was the second lowest number of new cars registered in May since 1992.
Only May 2020 – when the UK was in a coronavirus lockdown – was worse for the industry.
The SMMT attributed the decline to shortages of components which are reducing vehicle availability "despite demand".
Registrations of pure electric cars bucked the overall trend last month, with a 17.7 per cent year-on-year increase.
Electrified vehicles such as pure electrics, plug-in hybrids and hybrids accounted for three out of 10 new cars in May.
SMMT chief executive Mike Hawes said: "In yet another challenging month for the new car market, the industry continues to battle ongoing global parts shortages, with growing battery electric vehicle uptake one of the few bright spots.
"To continue this momentum and drive a robust mass market for these vehicles, we need to ensure every buyer has the confidence to go electric.
"This requires an acceleration in the rollout of accessible charging infrastructure to match the increasing number of plug-in vehicles, as well as incentives for the purchase of new, cleaner and greener cars.
"Delivering on net zero means renewing the vehicles on our roads at pace, but with rising inflation and a squeeze on household incomes this will be increasingly difficult, unless businesses and private buyers have the confidence and encouragement to do so."
Ian Plummer, commercial director at automotive classified advertising business Auto Trader, said: "Today's weak new car figures underline the lingering challenges for carmakers, as the war in Ukraine adds to the headwinds of a post-Covid shortage of semiconductors, and lockdowns in China.
"Even though the microchip shortage is easing a little, manufacturers are struggling to source critical components like wiring looms, which are a major Ukrainian export and hard to replace.
"While there are some signs of dented consumer confidence now dampening car-buying demand from its recent highs, the main issue in the new car market lies with supply rather than demand with most brands and dealerships boasting bulging orderbooks and buyers typically waiting many months for deliveries."
Alex Buttle, co-founder of used car marketplace Motorway.co.uk, said electric vehicle sales "provide a beacon of hope to the car market that things aren't all doom and gloom".
James Fairclough, chief executive of AA Cars, commented: “Things are going from bad to worse for new car sales as the ongoing shortage of supply runs into a new problem –weakening buyer demand.
“With the exception of electric vehicles, new car sales have been weak for much of 2022. At the start of the year this could be attributed largely to a chronic shortage of new vehicles arriving in showrooms.
“But as the cost-of-living crisis begins to bite, with consumers simultaneously grappling with surging fuel, energy and food prices, some are opting to postpone big ticket purchases like a new car."
* For the year to May Land Rover sales are down 42.1 per cent to 18,759, Jaguar has fallen 41.6 per cent to 5,532, but MG is up 83 per cent at 19,695.