Colleges say they and other providers need another pound;2 billion a year from 2010 if they are to meet the Government's aims for improving Britain's skills.
The Association of Colleges made the case for extra funding in its submission to the Treasury before Wednesday's budget.
Gordon Brown, the Chancellor, was expected to give education a Pounds 15bn-a-year boost, and colleges argue their track record on meeting the Government's targets means they should get their share.
John Brennan, the AoC's chief executive, said: "What we are saying to the Government is that the sector has delivered to a huge extent on the agenda we have been set for the last 10 years.
"It's everywhere you look - in quality improvement, expansion, specialisation, getting more young people and adults into the system, and shifting priorities. We are saying, `trust us to take forward the agenda you want to see'."
The bid to increase spending to pound;10.4bn is similar in scale to the AoC's last bid in 2004, when further education only received a pound;500 million increase.
Colleges say that decision was unrealistic given the demands government placed on the system and that it led to the massive cuts in adult education, when around 675,000 places disappeared.
But Dr Brennan said he believed the political climate has changed and that the Treasury may be more receptive this time, even as the rate of overall government spending slows down.
"There's been a shift in the awareness of the skills agenda and its critical contribution to economic success and social cohesion. There's an increased willingness on the part of ministers to show that they're going to tackle these issues," he said.
In its submission, the AoC conceded that funding for FE rose 48 per cent between 1999 and 2006, allowing for inflation. But it said the number of teenagers in FE was also at a 20-year high and ambitious targets for adult skills have been met.
The extra cash would be enough to pay for the pound;400m cost of universal participation in education or training between 16 and 18, as well as Pounds 600m on a more coherent system for 14 to 19-year-olds.
Expanding adult basic and intermediate skills to help meet the skills needs described by Lord Leitch in his report in December would cost another Pounds 600m while colleges are also asking for pound;350m in capital spending.
Colleges said that about pound;220m of the spending increase could be met by cutting bureaucracy, with pound;100m coming from the Learning and Skills Council, which the AoC said is bloated in comparison with its counterparts in Scotland and Wales or with the higher education funding body.
Another pound;120m is tied up in services provided to colleges by organisations like the Quality Improvement Agency. Colleges want to receive that money directly so they can choose how to spend it themselves.
Following the announcement of the overall budget for education on Wednesday, the Department for Education and Skills will have to decide between the competing claims of further education, schools and universities.