Dispute over pension scheme continues
Members of the trade union Community voted 88 per cent in favour of going on strike while the smaller GMB union said its members also approved strike action, statements said.
The union members are locked in a dispute with the company about its proposal to change their pension scheme.
"Steelworkers are determined to stand up to Tata," said Roy Rickhuss, general secretary of Community.
"We stand on the brink of the first national strike in the steel industry for over 30 years," said Rickhuss, also chair of the National Trade Union Steel Co-ordinating Committee.
The union, which did not give a date for a strike, said it was calling for Tata to return to negotiations.
Unions have been balloting some 17,000 members for industrial action. Results from the UCATT union was expected later on Friday while a ballot by Unite is due to close next Friday.
Tata Steel said in a statement that the vote was "disappointing" and that it was seeking to work with employees in a balanced way to tackle a pension fund deficit of up to $2 billion.
"We also remain hopeful that employees will avoid taking any action that damages our objective of building a successful and sustainable UK business capable of supporting a secure pension scheme."
An open letter to employees released earlier on Friday said Tata's UK operations as a whole were still losing money.
Profitability in Britain's steel sector has become difficult due to cheap imports and sluggish demand, which has yet to recover to pre-2008 levels.
The UK steel sector's labour, logistics and energy costs are higher even than mainland Europe, which itself struggles to compete globally.
The company's parent, India's Tata Steel Ltd, posted a $889 million quarterly loss on May 20, inflated by a hefty impairment on its UK business.