Angela Rayner peers down at me from newspaper clippings on the wall: there she is with Gordon Brown at a Labour party conference in 2007; that's her smiling with Ed Miliband at the leadership contest in 2010; and again, holding a placard at a TUC rally in March 2011.

As a full-time Unison representative at Stockport council, the photos of Rayner mixing with Labour high-fliers past and present are perhaps to be expected. What is more revealing is the framed photo of a serene Emmeline Pankhurst being arrested by the police on 13 February 1908.

"People underestimate me too," Rayner says, as I study the black and white photo of the suffragette. "I'm a pretty young woman, lots of red hair, and everyone expects me to be stupid when I walk into a meeting for the first time. I'm not stupid and most people know that now, but I still like to be underestimated because it gives me an edge. It gives me a bit of stealth."

As Stockport branch secretary, Rayner spends her working day, not to mention huge chunks of her own time, negotiating with senior council officers and councillors on behalf of around 4,000 Unison members. She wrangles with the local authority over pay and conditions, the impact of government spending cuts on council-run services and staff, as well as advising it on equality and employment matters. She also supports union members who are being made redundant, facing a disciplinary, or who have whistleblower-type concerns.

During the meetings I attend with her, she challenges and cajoles council leaders at every opportunity, quick to pounce on an issue, which might have negative fallout for the workers she represents. She reminds me that these public sector employees are not paper-pushing stereotypes, but hard-working public servants, many of whom are at the forefront of services – the social workers and home helps who assist the most vulnerable in society.

But I've chosen a tricky time to visit. The government has demanded Stockport council makes £50m worth of savings in four years. Now halfway through that time frame, the council is still trying to comply in a way that will have the least impact on its staff and the services they deliver. Rayner sympathises with the demands placed on the council, but only up to a point.

"I'm more than happy to work with them and I know they are not asking for the cuts themselves, but the managers here wanted to be managers and they are paid to answer the difficult questions. I'm there to remind them to consider the impact of their policies. We're in crisis management all the time now the austerity measures have kicked in. I've been in some horrible meetings where people are at risk of losing their jobs."

I'm allowed to sit in on meetings on the understanding that I will not report their content. I don't need to: little of it is newsworthy, but I gain a good insight into the mundane merry-go-round of life in a local authority. I learn the broad details of council budgets and such, but any juicy details on job cuts or spending plans are left for sub-meetings I won't be party to. Instead, I try to remain interested as human resources people, lawyers, leaders, deputies, as well as heads of almost every department you can think of, chat amiably. At least the building is interesting. I'm told it's where they filmed the BBC drama series Life on Mars.

I initially wonder if Angela herself is putting on a bit of a show as she takes the floor and launches into a series of questions during a "joint directorate" meeting. But I soon dismiss this idea: she's simply passionate ("you have to be for 20 grand a year") because she has been there herself.

"I grew up on a council estate and was pregnant at 16, only able to afford clothes from a charity shop. I was told I'd never amount to anything and would be living in a council house, on benefits with loads of kids by the time I was 30. That's not me, though I wouldn't judge someone if they were in that situation. But I have three lovely kids, live in my own house and have a great job – I've had to earn respect the hard way, starting as a home help when I left school."

By her own admission, Rayner at first "didn't know what a trade union was", but as one of the youngest home helps to be recruited in Stockport, she was constantly questioning management. Someone said she would make a good union rep and within a year she was a senior steward. "I successfully fought the privatisation of the home care service and then got to work nationally as a young members' officer. That's where I learned about politics and began to understand how everything, including the work I was doing, is part of a chain that leads up to government."

She was seconded from her job in social care to the position of assistant branch secretary for Unison where she is now in her second year – an elected role which has a one-year tenure. "I've faced a lot of challenges and you're always butting up against gatekeepers, but I am 31 now and I know how to be true to the people I represent. I know how training and support can transform them as people as well as improve the work they do, and how that benefits the local community."

Beneficiaries of her work are legion: from the many people who greet her as she walks through the council offices, to the home carer I meet later who, thanks to Rayner, has just completed a foundation certificate. She tells me: "I know everything now, including hygiene, nutrition, alcohol and drug abuse, and can deal with much more complex cases," she tells me. "I never thought I would get a degree of any type." Rayner says this view is typical in a sector that employs low-paid, predominantly female workers, but routinely fails to invest in them.

The fruits of Rayner's labour are also evident in her branch office. The shelves, already groaning under the weight of meticulously filed records, are covered with thank you cards from employees she has helped. "If I have a really bad day, I just look up at them," she says, "and remind myself what it's all about."

Rayner is proud that no social worker roles in Stockport have been cut and the jobs that have gone so far have been voluntary. But that does not mean services haven't been hit. "A lot of parental support services have stopped, free bus shuttles have stopped, and only the most urgent care cases qualify for home help now – meaning our carers have to deal with much more difficult cases. Helping keep everyone in a job but also ensuring all the public services are running feels a bit like doing a wedding on the cheap. The council probably feels the same way."

In meeting after meeting, if Rayner is not frantically taking notes she is asking probing questions about new reporting lines, staff changes and budgets. In one afternoon meeting, a senior member of the council answers query after query, before rolling his eyes and telling me: "She's a force of nature." A smile betrays his respect for the battling unionist sitting opposite.

Rayner has a warm relationship with the council leaders, but each knows which side they are on. This is obvious when she talks about grievance processes: "There are times when it's one of my members who has acted badly, but even then I blame management – after all, they recruited that person. Management created the mess, so it is up to management to sort it out, with the best possible result for the member I'm representing."

On the day I spend with Rayner there are no disciplinary hearings, but we do discuss the process over lunch in the council canteen. "You get genuine ones, where an employee has committed fraud or stolen something, and you try and do your best for them, ensure they might get a fair CV instead of a trip to the police station. We look for a corrective response not a punitive one.

"I'm not saying we've had this here, but there are cases where a manager has decided they want an employee out and you'll get one disciplinary piled on top of another until there are several – we call them red herrings. Management will try and make themselves look good by saying they'll waive all of them except one, then use that one remaining disciplinary to get rid of someone."

At the end of the day, Rayner sighs at her workload. There are union reps to be trained, updates from lawyers to read, and a business plan to be written, and that's barely scratching the surface.

At least she has a free weekend. The previous Saturday she had attended a Unison regional meeting and took Tony Lloyd MP to task for comments he had made about public sector pay restraint. "I didn't like his comments, so I asked him what he meant. I'm not sure he was expecting it." No doubt Lloyd – like most people in a position of authority who meet Rayner – quickly learned that you underestimate her at your peril.