Wajid Ali made the comment in an online petition he circulated.
Mr Ali stood for Parliament in Hemsworth at the 2019 General Election, polling over 5,000 votes and finishing in third place behind Labour and the Conservatives.
This year he was a candidate to be West Yorkshire's first metro mayor, as he stood for the Brexit Party’s offshoot organisation, Reform UK.
Mr Ali, who's been a taxi driver for 15 years, is a leading member of the Wakefield Drivers Association (WDA) union.
A longstanding critic of several Wakefield Council taxi policies, which he’s claimed have harmed the trade, Mr Ali set up a petition calling for one specific rule change in August.
In the petition, on change.org, he said: "Covid-19 and Brexit effect has already crippled the taxi industry and Wakefield Council must act now to safeguard our future."
Asked on Wednesday to account for this view given his political background, Mr Ali insisted he would still vote for Brexit, but that the government had yet to deliver on the promises it had made after striking a deal with the EU.
He said: “The government needs to work with local authorities to make sure that a fair deal trickles down to working class people.
"The promises they made, on things like NHS spending and spending on education, haven’t yet been delivered.
"The fact of the matter is we’ve a high unemployment rate and we’ve a shortage of truck drivers, potentially due to Brexit.
"The government needs to lock horns with the agencies and quangos involved in this.
"Brexit means we’ve got to be self-sufficient now. We have to help ourselves and we can't rely on the hands of other people."
Mr Ali, who was also a local election candidate in 2021 in Hemsworth for Reform UK, added: "It will take time for us to see the full fruits of Brexit and Covid hasn’t helped.
"Covid has been disastrous for the economic resurgence we’d expected.
"We are at the hands of national government on this."
Mr Ali's petition called specifically for Wakefield Council to relax its strict rules on vehicle emissions, which has left many drivers facing the prospect of having to replace their cars at great expense this year.
It's been signed by more than 230 people.
The council's licensing committee is due to consider a change, by temporarily suspending a ban on certain vehicles over the age of 10, at a meeting next week.
A council paper published ahead of the meeting acknowledged many drivers would face "additional hardship" in having to replace their vehicle and said the pandemic had "disproportionately affected" the local taxi trade.
Local Democracy Reporting Service