The cow, understood to be named Dundee Paradise, is the daughter of a clone in the US and was being raised on an unidentified farm in the Midlands, the Telegraph newspaper reported.
If confirmed, the dairy industry will likely appeal for calm among consumers amid fears milk from the cow could one day enter the UK food supply.
Dundee's mother was cloned from a two-time Supreme Champion at the World Dairy Expo, by Cyagra Clone, a US-based firm.
"When you have an individual this good you need to have more copies of her to realise her true value," the firm says. It claims to have sold a Paradise clone for $50,000.
Details of a Paradise relative in the UK emerged less than two weeks after food safety authorities in the US issued draft guidance on allowing meat and milk from cloned cows into the food chain.
The Food and Drug Administration cited several studies to again declare milk and meat from clones as safe as that from conventionally bred animals.
Its comments sparked fury from campaign groups, which claimed independent surveys showed around 60 per cent of Americans would not knowingly eat food from clones.
Europe's dairy industry remains cautious of a similar consumer backlash here, despite the opportunities cloning may bring to improve milk production.
"There's no intention as far as I know to have this introduced into the EU in the short or medium term," Joop Kleibeuker, secretary general of the European Dairy Association, told DairyReporter.com recently.
"We don't see acceptance of this from EU citizens, and we are producing products for our consumers."
Denmark is the only EU member state with specific legislation governing farm animal cloning.