In a blistering statement explaining his decision on Monday, Coun Akbar likened the whip system, which demands elected members vote with their party, to "corruption".
He said he would do "not what is best for my party, but for my residents", explaining he believed it was "impossible" to reconcile the two.
Coun Akbar became the first Conservative in decades to serve the normally safe Labour territory of Wakefield East, when he was elected last year in a shock result.
A fortnight later he voted against his Tory colleagues' Budget proposals, after criticising the party's suggestion that some local streetlights be switched off after midnight.
In his resignation statement on Monday, Coun Akbar said: "I have tried to remain amicable but I cannot represent the expectations of the party and reconcile this with the representation offered to my residents.
"The latter is my priority and always will be. It is impossible."
The 30 year-old solicitor said it was "undoubtedly clear that members quite simply vote as they are told", adding this is "an injustice to the people of Wakefield."
He added: "I am appalled that many fellow members of the council, whatever their party allegiance, do not have the backbone to to speak out and stand for real representation. Members are afraid of being deselected and fear for their political futures.
Coun Akbar said he'd been accused of "not being a team player" by party colleagues and that he'd "received grief for speaking out and representing my ward".
He added: "What I am describing here is akin to corruption and this is one of the worst predicaments that haunts councils across the country.
"The abuse of power by authority and public servants hinders the progress of our city.
"I will never be a part of such methods.
"I have made it clear that I cannot be held on a leash. I will not jump simply when I am instructed to be because that is the way the party operates."
Coun Akbar said that "members of my own community" had "spread malicious rumours" and "false allegations" about him.
He said he believed the majority of residents who voted for him last year, "voted for myself" rather than for the Conservative Party. But he said he "wholeheartedly apologised" to the "minority that did vote for the party".
Concluding his statement, he said: "Should there be an overwhelming majority of residents that feel I am no longer able to continue to represent the ward due to this matter I will resign from my position as a councillor and your representative of Wakefield East."
In response, Tory group leader Nic Stansby said: "I respect his feelings and good luck to him.
"I've known he wanted to be an independent for a while.
"Every single one of us stands for election because we want to represent the people who vote for us. He's not unique in that.
"We wish him well."
Local Democracy Reporting Service