The Labour politician, who is also the MP for Barnsley Central, and Conservative MP and Johnny Mercer, who is a former British Army officer, have put forward an amendment to the Nationality and Borders Bill, to waive fees for those with five years’ service.
Visas for foreigners who served in armed forces currently cost £2,389. Each member of their family also has to pay the fee if they want to remain in the UK, meaning it can cost a family of four nearly £10,000.
Mr Jarvis said: “Despite the sacrifice made by foreign and Commonwealth-born members of our armed forces, they face a shameful choice if they wish to make a home in the country for which they risked their lives.
“Pay thousands of pounds in Home Office costs or pack their bags. The result has meant some veterans have been handed massive NHS bills and threatened with deportation. This disgraceful treatment must end.”
There are around 9,000 foreigners serving in the British armed forces and around 500 leave every year.
The Government had promised to address the issue and launched a consultation on proposals to scrap fees for people who have served in the armed forces for 12 years, but not for their family members.
However, Mr Jarvis said that threshold is “unduly high” and the proposal would only alleviate costs “for a fraction of personnel”.
He added: “It offered nothing for families and veterans were thrown under the bus.
“Only meaningful reform will deliver justice so I hope all MPs – regardless of political affiliation – will do right by our service community and support my amendment.”
Mr Mercer, a former veterans minister, is hoping MPs will agree to waive the fees, when they vote on the amendment this week.
He said: “It’s something the Government promised it would do for a long time. This week is an opportunity for us to actually put that into action.”
In a statement, the Ministry of Defence said: “This Government is determined to address the issue of visa fees for the UK’s foreign born service personnel.
“We work closely with our non-UK recruits to make sure they are aware of how they and their families can settle in the UK, and the costs involved.
“Earlier this year we launched a consultation to see if more could be done. But the policy must be fair, the Jarvis amendment would unfairly impact service personnel who marry or have dependents from countries outside the UK.
“We are hugely grateful for the contribution of all our Armed Forces and will publish our response to the consultation when it’s complete.”