The job cuts would mainly fall at the plant in Scunthorpe, eastern central England, which employs 3,000 people and is the biggest steelworks in Britain.
Jobs would also be shed in Scotland, at the Clydebridge and Dalzell plants, said the BBC, Sky News television and The Daily Telegraph newspaper, which spoke of between 1,000 and 1,200 layoffs.
Tata Steel declined to comment on the reports but admitted it was facing difficulties in Britain.
"We've been talking about the challenges we're facing in the UK for many months -- surging imports, compounded by the strong pound and uncompetitive policy costs," a spokesman said.
Three weeks ago, Thai steelmaker SSI announced it was cutting 1,700 jobs and suspending production at the Redcar plant in northeast England owing to plunging steel prices on world markets.
Trade unions have urged the British government to intervene to save the steel sector, which employs 30,000 people in the country but faces competition from China as well as plunging prices.