The proposals, blamed on a downturn in the global gas and coal market, will mainly affect activities at sites in Stafford and Rugby, with 500 roles going at each.
The jobs are among 12,000 being cut worldwide as the company slashes costs.
GE currently employs 18,000 people in the UK and the cuts represent 6% of the workforce in this country. The company set out the plans to its staff on Thursday.
Mark Elborne, head of GE UK and Ireland (Other OTC: IRLD - news) , said: "Unfortunately, we believe that these changes are necessary to ensure that we can remain competitive and secure the future of GE Power in the UK."
GE said the changes were "driven by challenges in the power market worldwide".
It added: "Traditional power markets including gas and coal have softened.
"Volumes are down significantly in products and services driven by overcapacity, lower utilisation, fewer outages, an increase in steam plant retirements and overall growth in renewables.
"To get back to competitiveness GE Power needs to remove cost substantially from its business."
Its power division provides services and technology such as turbines, boilers and water systems to the industry.
GE said the restructuring would "simplify, consolidate and improve the efficiency of" research and development across its products.
But Unite union national officer ,Linda McCulloch, responded: "General Electric is in danger of cutting too far, too fast and leaving itself ill equipped to meet the challenges of the changing power generation market.
"These proposals will be a shock for General Electric's loyal workforce and deal a major blow to the Midlands' economy which will be deprived of highly skilled well paid jobs because of this announcement.
"Over the coming days and weeks, Unite will be supporting our members and scrutinising the company's business case as we fight to save as many jobs as possible.
"Unite will also be seeking guarantees from General Electric that there will be no compulsory redundancies and that there will be redeployment opportunities for workers wishing to stay with the business."