Six groups - including Rainbow Junktion and Leeds Anti Raids Action - organised the protest.
A Facebook page set up to advertise the event had more than 250 responses.
In the driving rain, more than 100 people turned up on Briggate to watch speakers and hand out leaflets and flyers on Saturday.
Many brought banners and posters and held flags.
One flag was emblazoned with the statement: "Make the rich pay for the cost of living crisis."
In a statement on the page, the groups said: "Following the recent announcement of a 54% increase of the energy price cap, plus the doubling of UK interest rates, the upcoming national insurance increase, and the rapidly rising costs of living, protests have been called to cut energy bills and tackle the cost of living crisis.
"We must stand up against the dangerous and deadly cost of living crisis, and demand the government roll back their plans and take action to cut energy bills, control skyrocketing rents, and increase incomes.
"This protest is a collective effort from grassroots community organisations from across different causes in Leeds coming together as a united front against austerity."
Protesters were asked to "bring signs, bring noise making devices" and "lots of friends".
The slogan of the protest is "nobody should have to choose between heating and eating. Everything for everyone."
Emily Carrigan - manager at Rainbow Junktion - addressed crowds gathering on Briggate.
She said: "Rainbow Junktion is a beautiful community café I have been running for five years.
"In those five years, and particularly in the last two years, we have seen a massive rise in the level of need in our community."
She said the pandemic, rising food and bill costs had all contributed to the difficulty residents are facing.
Concluding her speech, she declared: "Together we will not stop fighting, until we win".
One woman from group Bill Strike - who attended the protest - told the YEP the rising costs of living was "pricing people out" of living their lives.
Another woman held up a banner which read "Make the rich pay for the cost of living crisis".
Speaking to the YEP on Briggate, she said people were "really struggling".
"It is a protest against the upcoming cost and rise in cost of living", the woman said.
"People have had wage cuts for years and years, people are struggling as it is.
"It has been horrible.
"For many people during the pandemic, with the Universal Credit cut too.
"We need to keep doing this and make sure we get pay rises for everyone.
"I think it is fantastic that there are so many people that have come out in horrible weather.
"It shows the strength of feeling in the community of Leeds.
"It is not good enough and something needs to be done about it.
"This is going across the country.
"It is so hard for so many people, it is not getting any better."
The woman also called for the return of the £20 uplift in Universal Credit.
"It does not seem like a lot of money but it is, in the grand scheme of things.
"That £20 could feed a family for another day."
Owen Rees-Hattersley, 20 is a student at the University of Leeds.
He is a member of the Marxist society at the University.
He said he attended today to protest against the police and crimes bill which had "criminalised protest which is deemed too annoying".
"It is a massive attack on the democratic rights of freedom of speech and we should resist it", he told the YEP.
Owen said the UK is "going through a massive cost of living crisis".
"Wages are not going up enough to meet the rising cost of living", he added.
"Working people are being squeezed.
"It is going to make everyone's lives harder.
"I think the students in the UK right now are one of the most radical layers of society.
"We try to connect with them in our group and give them a voice for that frustration."
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