"We urge the government to avoid any hard Brexit", said Chief Executive Torsten Mueller-Oetvoes.
The company reported that its sales a year ago were down by 4.6% to 592,708.
MP for Meriden Dame Caroline Spelman and MP for Birmingham Erdington Jack Dromey both have Jaguar Land Rover workers in their constituencies.
It is to make £2.5 billion of cost savings and most of the cuts will be in the UK.
Armstrong said: "We are taking decisive action to transform the Ford business in Europe". The European Union has set lower limits for vehicle carbon dioxide emissions from 2021 that are pushing carmakers to include more electric vehicles in their future sales mix.
Most commentators have concluded that the chance of a no-deal Brexit have increased with the governor of the Bank of England recently describing the probability as "uncomfortably high".
At the time, it did not say how many jobs would be lost, although the Financial Times reported in December up to 5,000 jobs could go.
Unite national officer Des Quinn said: "Ford's workforce in the United Kingdom is world class in making and developing engines and gearboxes that are shipped all over the globe".
Unite national officer Des Quinn said: "Unite is positively engaging with Ford over its plans as we seek to safeguard jobs and look after the interests of all the company's employees in the UK".
"We expect the immediate impact on Ford's United Kingdom operations to be limited".
"The next stage of this transformation programme will begin with a voluntary redundancy programme in the U.K. This strategic review will create a leaner, more resilient organisation with a flatter management structure", the company added.
Beyond the £2.5 billion now being sought, rumours abound that Jaguar could be reincarnated as an all-electric brand in the not-too-distant future, better positioning it to deliver on future customer demand and lessening the burden it now places on the far-healthier Land Rover.
Jaguar Land Rover said earlier that its retail sales fell 4.6 per cent in 2018, citing uncertainty surrounding Brexit, the trade-war driven Chinese slump that lowered its sales in the country by 22 per cent, and consumer misgivings around the diesel engines that power much of its Land Rover lineup.
"Government ministers need to wake up and start doing more to support UK's vehicle workers".
"Government ministers need to wake up and start doing more to support UK's vehicle workers and their colleagues in the supply chain if Jaguar Land Rover's recent success is to continue".