It was felt the team, ranked fifth in the world, was not a credible medal challenger for the Tokyo Paralympics.
"Since London we have made massive progress and I believe we are good enough to medal in Tokyo," vice-captain Gavin Walker told BBC Radio 5 live.
It follows a similar campaign by fencing, which also lost its funding.
Wheelchair rugby has been awarded more than £6.3m over the last three Paralympic cycles and while Great Britain have won golds at European level over this time, they have never won a World Championship or Paralympic medal of any colour.

Conservative MP Justin Tomlinson has written to the Metropolitan Police after the publication of a photo online by the Guido Fawkes website.
Mr Tomlinson told the BBC that road safety was an important issue and the matter should be investigated.
Mr Khan, the Labour MP for Tooting, is a former transport minister.
The MP, who is thought likely to seek the Labour nomination for London mayor in 2016, was given a national award by road safety charity Brake this year.
Mr Khan told the BBC: "Allegations have been made that I glanced at my phone whilst in my car.
"I understand that a Conservative MP has now reported this matter to the Metropolitan police.  Of course I will be fully cooperating with any investigation."
Mr Tomlinson has written to Metropolitan Police Commissioner Sir Bernard Hogan-Howe about the alleged incident, reported to have taken place on Monday.
"I would be very grateful if you could investigate this further - road safety is a serious issue and those who make the laws should certainly not be above them," he wrote.
The Met confirmed it had received Mr Tomlinson's complaint.
A spokeswoman said: "We can confirm that today we have received a letter. We are currently assessing its content."

Play began 80 minutes late after rain with the tourists 66 runs behind and they lost Kraigg Brathwaite (8) to Charlie Hartley's fourth ball.
Kieran Powell (23) and Shai Hope (30) both spent time in the middle while Shimron Hetmyer made an unbeaten 43.
However, lightning and bad light forced the players off at 17:00 BST.
The West Indies face Derbyshire on Friday in their final warm-up match before they begin their three-Test series against England at Edgbaston on 17 August.
Great Britain Wheelchair Rugby has launched a fundraising campaign after losing its appeal against the removal of UK Sport funding.
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Shadow justice secretary Sadiq Khan has said he will co-operate with any investigation over claims he used his mobile phone while driving.
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The West Indies drew their tour match with Kent as weather impacted on their hopes of more batting practice on the final day in Canterbury.