Honking tractors carrying young farmers and a sea of people clad in tweed and wellies signalled the countryside had come to the capital on Tuesday to demand the scrapping of Labour’s budget changes to inheritance tax on agricultural businesses.

It would have taken more than plummeting temperatures and sleet to put off the thousands of food producers, many used to working in all conditions, from travelling from across the UK to Westminster.

Many had jumped on buses which forced their way through snow, while others had travelled the previous night and were quietly gossiping about Jeremy Clarkson, the Top Gear presenter turned farming celebrity, joining them for dinner.

The volume of attenders was unexpected, given the rarity of farmers taking a day off, let alone in such numbers. The Metropolitan police estimated there were 13,000 participants at the peak of the rally, leading them to prevent the crowd from marching down Whitehall for safety reasons.

Many farmers came with donations for the City Harvest food bank. Farmer Andrew Ward, one of the organisers of the rally, said it amounted to “tonnes and tonnes of food”.

Limited to a procession around Parliament Square, many protesters clutched signs criticising “Farmer harmer Starmer” as they waited to hear from politicians and Clarkson.

Despite the mainly good-spirited nature of the rally, there was gloom in the air as farmers discussed their deaths or those of their parents. Many feared that could be followed by the demise of their family farm.

“It’s a way of life,” said Penny Fortescue, 69, a sheep and arable farmer in Cambridgeshire. “We put up with the hassle every day because it’s our way of life, because we care about providing food. We wouldn’t do it otherwise, there isn’t any money in it really.”

Deluged by recent heavy rain, Fortescue now fears her way of life cannot be passed down to her daughter and son-in-law, if an inheritance tax bill eats up all their profits.

“I have cancer, my partner has cancer. I don’t know how long we are going to live. And if we try to hand the farm over within seven years, we can’t afford to live because it’s our pension,” she said. “We aren’t allowed to take money out of the business once it’s been handed over – so what are we supposed to do?”

Matt Swales, her son-in-law, said: “We are going to have to sell a portion of our land to pay the inheritance tax. That’s the reality of it.”

The message from the speakers was one of unity, amid a disagreement over whether the Treasury’s figures were accurate and worries that even medium-sized farms are at risk.

Spotting a political opportunity, the new Tory leader, Kemi Badenoch, brought her shadow environment, food and rural affairs team on stage to say they were the people who would “fight” for farmers. She called on those assembled to vote for her at the next election to reverse the tax changes. “Farming is not just a business,” she said. “It’s a way of life.”

The vast bulk of those in attendance were farmers, their families and supporters, but conspiracy theorists and far-right activists were present on the fringes. A contingent of activists from the Homeland party, a far-right group, appeared with a banner saying “Our Homeland needs Farmers” and posed for photos at the Cenotaph.

Many farmers attending the rally had spent some of their morning at the mass lobby event arranged by the National Farmers’ Union (NFU), and had booked meetings with their local MPs, many of whom are newly elected Labour parliamentarians.

Gary Yeomans, who farms goats near Abergavenny in Monmouthshire, met Catherine Fookes, the MP for Monmouthshire, along with eight other local farmers.

“She was sympathetic. Everyone had their say and kept their cool,” Yeomans said. “She said she wasn’t prepared to vote against the government, but said a group of 40 rural Labour MPs had got together.”

Others were left disappointed after they missed meeting with their MPs, either due to a large queue to get into the building where they have offices, or because their representative was not available.

Chris Robinson, a beef and sheep farmer from the Derbyshire dales, waited in vain for over an hour and a half to get into Portcullis House to meet his MP.

Meanwhile, Tom Rees from the Vale of Glamorgan in Wales, was frustrated to have been told in advance that his MP, Labour’s Kanishka Narayan, was away from Westminster on the day.

“I’m angry,” Rees said, adding that the newly elected Narayan is the parliamentary private secretary to the environment secretary, Steve Reed. “He needed to front up to this.”