Honda said individual discussions will be held with workers at the Swindon factory following the announcement, while union officials have been briefed about the plans.
Around 150,000 cars were built last year in Swindon.
A third of the cars are sold in the UK, with the rest being exported to 26 countries, mainly in Europe.
Honda builds the Jazz, Civic and CR-V models in Swindon.
Honda says 'formal consultation' will take place to consider cuts
Sustained conditions of low demand in European markets make it necessary to re-align Honda's business structure.
As such, Honda of the UK Manufacturing (HUM) will enter into formal consultation with its associates to consider these changes and the proposal that it will reduce the workforce by 800 associates by spring 2013."
– Ken Keir, executive vice president of Honda Motor Europe
Japanese car giant Honda has announced it is to cut 800 jobs after a slump in demand across Europe. Workers at the firm's plant in Swindon, which employs 3,500 people, were told the news this morning.
Honda, which has been making cars in the UK since 1992, has never had job losses before in this country, but it said demand for cars in Europe, including Spain, Italy and Greece, had fallen by a million in the past year.
The company gave the statutory 90-day notice of consultation and said it would seek to avoid compulsory redundancies.
The Business Secretary Vince Cable is in Swindon today as Honda introduce its latest car.
500 new staff have already been recruited at the plant to produce a range of new models and engines. It's part of a 267 million pound investment programme.
500 staff are starting work at Honda in Swindon today. The Japanese car giant is introducing a second shift in response to growing demand. The company predicts the move will double production at the plant, with 180,000 cars coming off the production line by the end of the year.
The new jobs reflect growing demand for Honda's new Civic family hatchback Credit: ITV West
It brings the total of workers at Swindon to 3,500. Last year, staff were on reduced hours after the Japanese earthquake and floods in Thailand affected the supply of parts.
Rise in profits is a change of fortune for Honda Credit: ITV Westcountry
Honda, which has a factory in Swindon, has announced a 61 percent rise in profits in its first quarter results.
More than 3,000 workers at the Swindon plant had to work reduced hours last year after the Japanese tsunami and floods in Thailand affected the supply of parts.