Fujitsu said the plan was to streamline its operations and make it more competitive in a global information technology market.
The layoffs amount to around 13 per cent of its workforce in Britain and Ireland, where it claims to be the biggest Japanese employer with some 14,000 staff.
Fujitsu insisted the announcement was not linked to Britain's vote in June to leave the European Union.
The programme will enable Fujitsu to "better support customers in the era of digital transformation", the company said.
"As part of the programme, Fujitsu plans to streamline operations in order to remain competitive in the market.
"Proposed measures include changes which would result in a reduction of up to 1,800 jobs in the UK."
A spokeswoman told AFP that no jobs would go before 2017 and Fujitsu would be able to give clearer details on job losses next year.
Shares in Fujitsu soared last Thursday on news it was considering merging its struggling personal computer division with China's Lenovo, the world's biggest PC maker.
Once mighty Japanese firms have been selling off assets in recent years as they struggle to reorganise in the face of stiff competition from lower-cost rivals abroad, including in China and South Korea.
Established in 1935, Fujitsu describes itself as the world's fifth-largest IT services provider and the biggest within Japan. It says it has around 156,000 staff worldwide.
Within Britain and Ireland, it claims to enable processing of 2.8 million passports and more than 10 million driving licence updates every year.
"Fujitsu's main UK subsidiary made USD 104 million profit last year and we see no reason for these job losses," said the union's national IT officer Ian Tonks.
"Unite will be doing its utmost to fight for these jobs, as well as giving our members maximum support at this very worrying time."
Unite said workers would be affected at Fujitsu's major sites which include Belfast, Bracknell, Crewe, Londonderry, Manchester, Stevenage, Wakefield and Warrington.
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