Penny Andrews has a chequered CV for a 31-year-old. She struggled in her first job as an editorial assistant, which ended in redundancy. Her next employer disciplined her for publicly discussing colleagues' pay rises, while another let her go for lacking initiative. Others insisted she had no common sense and was "ditzy". Both descriptions are inaccurate, she insists.

Andrews comes across as sharp and self-aware, with a perceptive intelligence. Currently studying for a degree in IT and communications with the Open University, she recalls: "I never fitted in. I was an observer rather than part of the team – 'the tribe' as I thought of them – because I never understood the unwritten rules."

The source of her difficulties was a mystery to everyone including her, until she was diagnosed with Asperger syndrome last year – late diagnosis is typical of females with autism which includes Asperger syndrome. Andrews says she always knew she was different and that the diagnosis was a relief.

"I just thought I was a terrible person who couldn't make a job, or anything else, work out. I dropped out of two previous university degree courses because of similar problems around fitting in and communication," she says.

"Now that I understand more about myself and my autism, I want to raise awareness among employers of what it is; that it isn't a bad thing, just a different thing. I would love a job that took my skills and harnessed them, because of who I am, and what I am, rather than in spite of it."

She says she can be "bubbly" if she tries really hard, but it exhausts her as it is learned behaviour rather than something that comes naturally. "If I was myself, everyone would think I was a boring cow."

Andrews, who wants to secure a place on a graduate scheme for librarianship when she has finished her degree, is one of 100 ambassadors for the National Autistic Society (NAS) and is helping promote its new Undiscovered Workforce campaign.

Launched in the House of Commons in March, with cross-party support, the campaign is aiming to increase employment opportunities. "We need MPs to help us show how much people like me have to contribute," she says. "One in every 100 of their constituents has autism, after all."

Job interviews are a huge barrier to employment because of the requirement for good communications skills. Just 15% of those with autism have full-time jobs according to NAS research, while another 9% are in part-time work. These figures compare unfavourably with the 31% of all disabled people in full-time work in the UK, while more than a quarter of all graduates with autism are unemployed, the highest rate of any disability group nationally.

The key difficulties are social interaction, establishing relationships, lack of emotional reciprocation (which can give an impression of indifference), difficulty with flexibility of thought, forward planning and thinking in abstract ways. The upside, however, is equally considerable.

According to Jane Asher, who is president of NAS, autistic people often make better employees than those known in the word of autism as "neuro-typicals" – ie, the rest of us. She explains: "People with autism tend to be very reliable and punctual. They like routine, and most won't mind doing repetitive tasks. Many are very good with maps and figures. They are usually scrupulously honest – they just don't have the guile to be anything else, and they can't lie.

"There is a huge lack of imagination on the part of employers who are missing out massively by ignoring this untapped pool of labour."

Proponents like Asher say it's not about pushing the charity card – or even corporate social responsibility – but about a real benefit to employers of taking on loyal, talented people with unique skills. They also say that what is good for those with autism, can be good for us all; for example, the need for employers of autistic people with autism to brush up on communication skills, which can be beneficial to everyone.

Charles Manby, managing director of telecommunications, media and technology for Goldman Sachs Investment Banking, is a keen supporter of integrating people with autism into the workplace. "We employ an autistic guy to run our database and research programmes, and he's really competent and well organised," Manby says. "His communications skills are poor, but we're all used to him and he's used to us, so he talks and chats.

"Graduates come and go – they stay between two to three years, but he is always there, so, hopefully, our graduates will have gathered a good impression, and, through word of mouth, might end up employing someone like him."

Manby hopes initiatives like this will encourage people to see normality in employing autistic people. "We've taken on about 60, and we are very glad to be doing that from a business point of view."

Employers open to taking on people with disabilities are increasingly being known as "disability confident businesses".

A nurse with Asperger syndrome called Kay, says: "If everyone was like Charles, we'd all be fine. He's what I call 'Aspie-friendly' – he gets us. So many employers don't, and we need to educate them."

Like many non-medics working in healthcare, Kay got into trouble at work for failing to observe a well-established hierarchy and is now awaiting a disciplinary hearing, having been suspended on full pay for two years. She says she is going out of her mind with boredom.

A care assistant (who wishes to remain anonymous) got into hot water for asking a surgeon who walked out of theatre and straight past the hand-washing area, if he had washed his hands. "He took offence," the care assistant says. "I thought I was doing the right thing. The anti-MRSA posters are all over the hospital."

The Autism Act 2009, a response to continued poor employment rates for people with autism, was the first-ever piece of disability-specific legislation to be passed by government. The Department for Work and Pensions and the NAS have since published a guide for employers, Untapped Talent, on taking on autistic people which highlights their aptitude for problem-solving and attention to detail, high levels of concentration, reliability, loyalty, excellent memory and detailed factual knowledge, retention, resourcefulness and technical ability.

Everyone is different, however, and the minister for Welfare Reform, Lord Freud, recalled a well-worn quote during his speech at the launch of the Undiscovered Workforce, namely "Once you've met someone with autism … you've met someone with autism."

Employers can put practical measures in place to help, such as providing purple filters for computer screens – a special tool that filters out the bright colours and information overload which overwhelm many autistic people.

When admin worker Kay Ribbons asked for a purple filter, however, colleagues accused her of "milking it", using her autism to gain special treatment. Ribbons, who is now unemployed, said: "It's just ignorance, but they really thought I was singling myself out to get something extra, whereas the reality was that I needed it to do the job properly.

"My time in work so far has been very stressful, as I've constantly had to defend and explain myself all the time. If employers were more aware, I'd be able to work in an environment that supported me, rather than one that battled against me. All I want to do is work, and I have a lot to offer, but I can't seem to fit in anywhere."

Sadly, her story is extremely common, with most autistic people experiencing something similar.

Guy's and St Thomas' hospital in London set up an employment initiative last year called Project Search, specifically to help people aged 18-30 with autism to gain work experience serving food to patients on wards. Of the six people the pilot has trained so far, two now have permanent jobs at the hospital.

Chris McGuire, head of the Guy's and St Thomas' catering services, says: "People are needlessly frightened of autistic people because they are an unknown to them. Autistic people actually make great employees because they follow instructions to the 'T'. They like continuity, and they won't make their own decisions, so there are no loose canons."

McGuire admits life working with autistic people can be a learning curve for all involved. "Sometimes funny things happen, like the 20-year-old who tried to join a doctors' meeting because he had observed something about a patient," he recalls.

"But, mostly, autism can be a valuable asset and the NHS and the private sector need to do a lot more to break down the ignorance that is preventing autistic people from working."

• This article was amended on 10 April 2012 to clarify some details about Penny Andrews' employment history and diagnosis.