Britain is facing a shortage of workers with programming skills, fuelled by poor-quality training courses in universities and colleges, which has left firms in fields ranging from advertising to Formula 1 struggling to recruit.

Leading companies interviewed for a new Guardian series say they require staff at a senior level to be computer literate, combining digital skills with the ability to lead a team. But they face delays in hiring the right staff, or have to give new employees extensive training because many computer science courses are nothing more than "sausage factories".

Ian Wright, the chief engineer for vehicle dynamics with the Mercedes AMG Petronas Formula One team, said: "There's definitely a shortage of the right people. What we've found is that somebody spot on in terms of the maths can't do the software; if they're spot on in terms of the software, they can't do the maths.

"It's a question of time – how long it takes to find people. That can mean months down the road. This is a fast-moving business. Every two weeks in the racing season you're out there, everyone seeing how well you do."

The government is poised to overhaul the teaching of computer science in schools, and Michael Gove, the education secretary, is due to outline the coalition's approach to digital skills on Wednesday.

Gove is keen to see a greater emphasis placed on training children to be technologically adept, and believes that in the past schools have focused too much on acquiring expensive kit that has rapidly become obsolete.

The Guardian has spoken to firms involved in games design, outsourced IT support and visual effects that are critical of the scarcity of properly trained recruits. In a series of articles, Guardian writers will explore the state of computer science teaching in schools, look at the use of technology in teaching, and see how other countries are faring in comparison to Britain.

In higher education, although universities such as Bournemouth are praised by employers for working closely with industry, other universities and colleges have been criticised by businesses for running a significant number of "dead-end" courses in computer science, with poor prospects of employment for those enrolled.

Figures for the graduate class of 2010 show computer science graduates have the highest unemployment rate of any undergraduate degree, at 14.7%.

There is particular criticism of specialised video games and effects courses. In 2009, just 12% of graduates from video games courses found jobs in the sector within six months of graduating. Employers in the games industry say graduates of these courses lack expertise with the relevant gaming platforms, have poor technical skills in areas such as maths and programming, and lack management skills.

Ian Vickers, the managing director of Managed Enterprise Technologies, an IT support firm that works with businesses including food manufacturers and insurance companies, said: "A lot of training agencies have been focused on making money, [and are] not interested in providing young people to be fit for work. It's like a sausage factory.

"They're not interested in how successful they are, being fit for purpose for employment. All of the training organisations are guilty of getting young people on to the courses so they can get the funding from government."

In a highly critical report last month, school inspectors warned that too many information and communication technology (ICT) teachers had limited knowledge of key skills such as computer programming. In half of all secondary schools, the level many school leavers reach in ICT is so low they would not be able to go on to advanced study, Ofsted said.

High-flying students are often not stretched while many pupils spend computing lessons repeating tasks asked of them a year ago.

There has been a dramatic fall in the number of pupils taking a GCSE in ICT over the past four years. In 2011, 31,800 pupils took the GCSE, compared to 81,100 in 2007.

Labour's shadow education secretary, Stephen Twigg, said in a speech last week that schools must embrace technology as a "vital tool of learning".

Wright, of Mercedes AMG Petronas, said the lack of good candidates meant his firm had to make compromises, devoting time to training people up in maths or software skills.

A growing demand for computer skills has not been matched by a supply of skilled recruits, firms say. The transformation of businesses by the internet has increased the need for senior staff to be skilled at using new technology.

Jason Goodman, founder and chief executive of advertising agency Albion, said: "The sort of business we are in 2011, and when we started nine years ago, is radically different … When we started, we had a much bigger design team; now we have a much bigger technology team."

Trialling ideas through social media has taken the place of carrying out research, Goodman said, giving the example of a pilot which had 70,000 "likes" on Facebook: "Then it became clear that was it, we were going to develop an offline campaign."

He said: "You've got to have a very tech-savvy team, who understand how an idea is executable, rather than having to ask anybody about that."

Fierce competition for scarce talent has led to long delays in recruitment, Goodman said.

"We spent two years looking for a tech director, looking in the UK, Europe, in the States. The US has got a much bigger English-speaking pool of talent. We're doing a lot of this work for 12 months longer than we have to."

The problem is magnified for smaller firms competing against household names. Companies such as Microsoft, which has around 3,000 candidates chasing 40 graduate places annually, say the problem for them is more one of sifting applicants, but a smaller business will often have to reach a compromise on conditions with a promising applicant – agreeing to flexible working packages, or signing over intellectual property rights.

Kim Blake, the events and education co-ordinator for Blitz Games Studios, said: "We do really struggle to recruit in some areas; the problem is often not the number of people applying, which can be quite high, but the quality of their work.

"We accept that it might take a while to find a really good Android programmer or motion graphics artist, as these are specialist roles which have emerged relatively recently – but this year it took us several months to recruit a front-end web developer. Surely those sorts of skills have been around for nearly a decade now?

"Programmers of sufficient quality remain hard to find in all their varieties, whether it's tools specialists, game-play programmers, audio programmers, network programmers."

While her firm was prepared to invest in training young people, there were often fundamental flaws in new employees' school education, Blake said.

"There is still a basic level of maths and physics skills, in particular, which are alarmingly absent in all too many candidates."

While recruitment delays have never led to them turning work down, "projects have certainly been delayed or progressed more slowly than we thought," Blake said.

Alex Hope, who co-authored a review of digital skills for the video games and visual effects industries, emphasised the value of a combination of relevant skills and a strong track record of academic achievement.

Hope, managing director of the visual effects firm Double Negative, said: "In Harry Potter [and the Half Blood Prince], the opening sequence has Death Eaters flying across the river Thames, destroying the [Millennium] bridge between St Paul's and the Tate Modern.

"The way you create that is people who understand computational fluid dynamics, they know how water moves. They take the physics that's used in modelling rivers and the flow of water and apply that in our world. People doing it need an artistic sensibility as well. An understanding of maths and science is fundamental to many of the disciplines in our industry."

Wright supported the need for better maths and science education. "We use maths and physics all the time," he said. "You need to understand them to do the kind of things we do. We're looking at very small gains all the time, [so] your accuracy of simulation has got to be very high. Otherwise you can't make a judgment as to what you're doing. If we put a device on the car, then we need to know what performance advantage it will give us and need to know this very early in the design process. This is measured in fractions of a second. It's measured in less than tenths of seconds."