Unite the union believes that up to 1,600 jobs at HP's UK sites could be lost as a result of the company's restructuring plans.
HP revealed plans to cut 27,000 jobs worldwide by 2014 last night, as it announced its quarterly financial results.
According to Unite, the number affected would equal eight percent of HP's 20,000-strong workforce in the UK. The union has around 4,500 members working for HP, including computer programmers, desktop support, software engineers and software architects.
However, HP has not yet revealed a country breakdown of the redundancies, and said that the 1,600 figure was "speculation".
It is understood that the 27,000 job losses will include those who volunteer for early retirement. A consultation on the remaining job losses will begin in the UK and Europe over the coming months.
Kevin O'Gallagher, Unite's national officer for IT and communications, said: "We will be working with the PCS (Public and Commercial Services) union to use every means possible to protect these vital and high-skilled jobs.
"We hope to arrange meetings with the senior management, both in the UK and with the global business leaders, as soon as possible to set out our alternatives."
He added: "HP is still a highly profitable company which is, we believe, simply aiming to cut costs to increase both its market share and profits, while showing scant regard to its loyal and dedicated workforce."
HP's UK sites are based in Bracknell, Berkshire, Bristol, Derby, Manchester, London, Dublin and Sheffield.
Meanwhile, Autonomy founder Mike Lynch also announced his departure from HP after less than a year under the ownership of the US company.
Sources close to the situation said that he is following in the footsteps of the 20 percent of all staff and entire management team who have left Autonomy since HP took over in October.