"We had nowhere left to put them," says Richard Parker, Chichester's principal. "But we never turn students away, especially in employment-related work."
Instead, the college found vacant warehouse space on a nearby industrial estate. And within weeks it was running bricklaying courses.
"Since Christmas, we have had over 250 enquiries from people wanting plumbing courses," he says. "And again we have the same view - we will not turn them away."
Chichester is one of seven FE colleges in Sussex to adapt itself to the needs of local employers in an initiative called Colleges For Business, spearheaded by Sussex learning and skills council. The first phase is to be launched this summer.
Colleges are working with one of the UK's largest chambers of commerce, Sussex Enterprise, which has close links with 10,000 employers. The chamber will train a "sales force" of brokers to bridge the gap between employers and education.
Some colleges are already looking at setting up "mini-boards" largely staffed by local business people to help students focus on business needs.
The next step is for colleges to work with private training providers and the area's three universities to supply the skills Sussex so badly needs.
Henry Ball, executive director of Sussex learning and skills council, cites Chichester as a good example of how the FE sector is responding to employers' demand. The skills council has pledged to implement "the most coherently planned and focused development of the Sussex workforce ever undertaken", giving every employer access to skills training and development. Mr Ball says: "I think we're on the verge of something really important in terms of a major development for supporting the skills needs of local industry.
"It is early days yet, but the buy into this has been amazing. This isn't just about colleges - they can't do it on their own. They have to work in partnership with a number of others."
Making these changes has, in Mr Ball's words, involved "a series of bold steps" to bring changes to that relationship. When the learning and skills council started two years ago, it found an uneasy relationship and little understanding between employers and education in Sussex. "All colleges were constrained by a number of issues," says Mr Ball. "How they're funded to deliver training doesn't always sit easily with how the employer would like to access financial support for training.
"There was always the issue about flexibility. Doing it when the employer wanted and where they wanted. There's also that issue of ambience in a college - colleges are quite generalist in that they cater for young people through to retired people.
"That generalist approach didn't sit well with many businesses that felt they wanted a more dedicated and purposeful approach to meeting their specific needs."
Sussex LSC began with an analysis of employers' needs. The construction industry emerged as a big challenge with the prospect of new housing development and a huge skills shortage. The public sector, one of Sussex's largest employers, health and social care - with large numbers of care homes - and air travel and transport based around Gatwick - all of these needed skills training.
It also identified four generic issues affecting the local area: the rural economy, management training, information and communications technology, and basic skills training.
In its first months, the council met college principals, Sussex Enterprise and the Learning amp; Skills Development Agency and began to look at ways colleges could adapt to meet business needs.
It also pondered the problem of poor-quality private training providers. It had many small contracts with trainers, some of which it felt would fare poorly if inspected. Two of its big centres - Brighton and Hastings - provide very few courses that are work-based.
So the council set about cutting the number of companies it paid to provide work-based learning - from 75 down to 23. But despite this, numbers in work-based learning in Sussex have increased by 6 per cent.
"What we wanted to do was reduce it to those that had the capacity to deliver at the volumes and quality we required. So we took quite a tough series of decisions," says Mr Ball.
He envisages networks of colleges, private providers and universities working together to fulfil the skills needs of employers. And this fits into the wider picture of the 14-19 agenda connecting schools, colleges, employers, Connexions and the voluntary sector to provide young people with new career paths.
"Here in Sussex, particularly in East Sussex, the GDP (gross domestic product) per head is one of the lowest in England. Hardly anyone ever begins to appreciate that startling statistic - everyone thinks it's the affluent, soft South.
"And we see the skills agenda as our contribution toward doing something about that - and helping to raise skill levels and therefore productivity levels in our patch."