Nine hundred jobs will be lost at the firm’s plant in Scunthorpe. The remaining 270 jobs will go in Scotland.
The industry blames cheap Chinese imports for a collapse in steel prices.
The jobs going at Tata Steel are in part of a division that the company failed to sell earlier this year.
Buffeted by collapsing prices and the strong pound, Indian-owned Tata has decided to cut back its UK operations.
Tata’s steel plant in Scunthorpe, which employs 4,000 people, is one of the largest in the UK.
But two mills in Lanarkshire are also affected raising concerns about the future of the industry in Scotland.
The plants under threat are the Dalzell plate rolling works in Motherwell, which opened in 1872, and Clydebridge, in Cambuslang, which has been operating since 1887.
The plants became two of the giants of Scottish industry, with Clydebridge providing steel plates which were formed into many of the most famous ships built on the River Clyde.
The industry was at the heart of many Lanarkshire communities and Motherwell Football Club still use the nickname “the Steelmen” in tribute to the workers who supported them.
Analysis: Anthony Reuben, business reporter
It’s been a tough few weeks for the UK manufacturing sector.
Manufacturing accounts for about 10% of the output of the UK economy. But most of the big headlines have been about one sector: steel, with Thailand’s SSI closing down in Redcar and India’s Tata shedding jobs.
The industry in the UK blames this on relatively high electricity prices in the UK for such energy-intensive businesses, compounded by the extra cost of climate change policies.
It says that the government’s policies to compensate steel companies for such extra costs have been coming in too slowly.
There are allegations that the Chinese steel industry has been selling steel in the UK at unrealistically low prices.
Also, the European Union is unusually strict about state aid to iron and steel companies. So it is a particularly difficult time for the UK steel sector, which is having an even harder time than manufacturing as a whole.
John Park, assistant general secretary of trade union Community, said: “Our immediate thoughts are with the workers and their families who will be affected by this announcement.
“Community representatives will be looking to sit down with the company, to understand the detail and to look at all alternatives that save jobs and uphold our principle of no compulsory redundancies. We will also be putting in place advice and support for our members who are affected.
“The government should hang its head in shame at today’s news. The cruel irony of the prime minister welcoming the Chinese premier as UK steel jobs are cut, partly due to Chinese steel dumping, will not be lost on the UK’s steelworkers and their communities.”
He added: “We have been saying for years that more government action is needed to support UK steel as a vital foundation industry. We have made clear that the situation is urgent. Despite these warnings, the government has been too slow to respond.”
Business Secretary Sajid Javid told the House of Commons there was “no straightforward solution to the complex global challenges facing the steel industry”. But he added the government had “no intention of standing by”.
“Today was an important opportunity to bring the key players together and we now have a framework of action,” he said.
The business secretary said the government had already promised £80m to help those affected by steel plant closures and had set up a task force to look at how to help the UK steel industry and its workers.
“We are taking steps to ensure there is a future for the UK’s steel industry,” he said.
But he pointed out there was a global steel surplus which was pushing prices down, adding there there were limits to what the government could do in response and that no government could dictate the price of steel or foreign exchange rates.
He said the government was committed to major infrastructure projects and he was “determined that the UK steel industry should play its role in its delivery”.
In the 1970s, more than 200,000 people were employed in the UK steel sector, but the number now stands at just 30,000. Unions say that one in six of those jobs is now under threat.
The collapse into administration of parts of steel processing firm Caparo on Monday followed the closure last month of the SSI steel plant at Redcar, with the loss of about 2,200 jobs.
The industry has blamed a flood of cheap steel being dumped on the global market by Chinese manufacturers.
Mr Cameron said: “The British government is doing everything that we can, and every issue that we can take up, we will.”
But Roy Rickhuss, general secretary of Community, said: “We have had a succession of ministers, and now the prime minister, saying that they will ‘raise’ the issue of Chinese steel dumping, which we know is impacting on the UK steel industry and the global steel price.
“The prime minister needs to do more than ‘raise’ the issue. He needs to tell the Chinese premier what action he’s going to take to stop Chinese steel damaging the future of a vital foundation industry in the UK.”
Caparo administrators PwC said workers would be paid and briefed on developments, adding: “It is business as usual while the administrators’ review gets under way.”