Unions reacted with shock and anger at the company’s decision, taken at a board meeting in Mumbai.
Labour has led calls for the Government to intervene to save the industry from total collapse.
Shares in the company climbed more than 1% when trading opened in India on Wednesday.
In a statement issued in Mumbai, Tata said it noted with “deep concern” the deteriorating financial performance of its UK subsidiary in the last year.
“While the global steel demand, especially in developed markets like Europe has remained muted following the financial crisis of 2008, trading conditions in the UK and Europe have rapidly deteriorated more recently, due to structural factors including global oversupply of steel, significant increase in third country exports into Europe, high manufacturing costs, continued weakness in domestic market demand in steel and a volatile currency.
“These factors are likely to continue into the future and have significantly impacted the long term competitive position of the UK operations in spite of several initiatives undertaken by the management and the workers of the business in recent years.”
Tata said it had suffered “asset impairment” of more than £2 billion in the last five years.
The board unanimously concluded that a plan aimed at saving plants including Port Talbot in South Wales was unaffordable, said Tata, adding it had been in “deep engagement” with the UK Government in recent months seeking its support to achieve the best possible outcome for the UK business.
“Following the strategic view taken by the Tata Steel Board regarding the UK business, it has advised the board of its European holding company ie Tata Steel Europe, to explore all options for portfolio restructuring including the potential divestment of Tata Steel UK, in whole or in parts.”
A joint statement from the UK and Welsh governments released by the Department for Business, Innovation and Skills said: “This is a difficult time for workers in Port Talbot and across the UK.
“During the review process, we remain committed to working with Tata and the unions on a long-term sustainable future for British steel making.
“Both the UK and Welsh governments are working tirelessly to look at all viable options to keep a strong British steel industry at the heart of our manufacturing base.”
Labour said ministers had “gone missing “ while the crisis gripping the steel industry has unfolded.
Party leader Jeremy Corbyn urged the Government to intervene as a matter of urgency, possibly by taking a public stake in the industry.
There were calls for the Welsh Assembly to be recalled from the Easter recess to discuss the crisis.
Union leaders travelled to Mumbai where the Tata board met to discuss the company’s loss making UK business.
They had been hoping Tata would agree to a turnaround plan to keep steelmaking in Port Talbot and other UK plants. The news will affect other Tata sites including Rotherham, Corby and Shotton.
Tata announced over 1,000 job cuts in January, including 750 in Port Talbot.
Thousands of steel jobs have been lost in the past year, with companies blaming cheap Chinese imports and high energy costs.
Mr Corbyn said he was “deeply concerned” at the news, adding: “Ministers must act now to protect the steel industry and the core of manufacturing in Britain.
“It is vital that the Government intervenes to maintain steel production in Port Talbot, both for the workforce and the wider economy, if necessary by taking a public stake in the industry.”
Labour MP Stephen Kinnock, who is with the union delegation in Mumbai, had urged Tata to “hold its nerve “ in the face of the problems it was facing. He was critical of the Government for not sending a minister to lobby the Tata meeting.
Business Secretary Sajid Javid is in Australia on an official trip.
The decision came completely out of the blue to union officials.
Dave Hulse, national officer of the GMB union, said: “This is absolutely devastating news for all our members, their families and the local communities. Tata has let the whole of the UK steel industry down.”
Unite general secretary Len McCluskey said: “This is a very dark day for the proud communities and a proud industry which is now on the verge of extinction in this country.”
Roy Rickhuss, general secretary of Community, said: “We travelled to Mumbai to secure a future for steel making in South Wales and we are disappointed that the future remains uncertain, not just for Welsh steelworkers but for thousands more workers in Tata’s businesses elsewhere in the UK.”