It may be that your own organization call allocate funding from within its reserves.
What other organizations within your area would benefit from residents who do not have English in their communicating abilities? These may typically include other charitable organizations focusing on the needs of the community and Housing Associations. You could approach them with a view to sharing both the costs and the benefits.
If you do not mind brand names being displayed during ESOL courses, you may consider approaching businesses with a view to them sponsoring such courses and in addition, it would be an excellent public relations opportunity for both your organization and the sponsor. This article may be of use: http://www.raisingfunding.co.uk/how-get-corporate-sponsorship-for-fundraising.html
Many non-profit organizations take advantage of the services of professional fundraisers. These fundraisers may be paid for their services either through fees unrelated to the amounts of money to be raised, or by retaining a percentage of raised funds (percentage-based compensation).
Many non-profit organizations nonetheless engage fundraisers who are paid a percentage of the funds they raise. It should be noted that the term "professional fundraiser" is in many cases a term referring to third-party firms whose services are contracted for; whereas "fundraising professionals" are often individuals on staff at charitable non-profits. Although potentially confusing, the distinction is an important one to note.
Whilst it is understood that your organization may well be not for profit, the learners could be recruited with a view to paying their own way. Depending on numbers, this could be as little as £2.50 per week where your premises are used for classes. The learners would need to understand that a non-refundable deposit would be required to ensure costs are met.