Answer

It would be better to work the costs into a long-term project, because you could still be in the same situation in two or three years and the funder would be less inclined shovel more money in if there is little evidence of sustainability.

 However, saying that, I can sympathise with the situation of charities with increasing overheads, so you would need to look for the few funders who fund running costs.

The one I know about is the Lloyds TSB (see details below), and you will find details of other potential funders in the attached Grantfinder search (the ones to look for are the funders that support voluntary sector infrastructure or social enterprise: http://www.socialenterprise.org.uk/Page.aspx?SP=1954):
 

LLOYDS TSB:

Grants are available to support underfunded charitable organisations in England and Wales that improve the lives of people in local communities, especially those who are disadvantaged.  There are three grant programmes which are: The Community Open Programme; and The Community Priority Programme.

NECESSARY QUALIFICATIONS OF APPLICANT       

No stipulations are made with regard to the number of employees or size of an applying organisation       

Location.           England and Wales 

CRITERIA

Applications may be made at any time. Must be a viable project        Funds are limited, therefore, grants are discretionary. Separate criteria apply for each of the three grant programmes (see Detail report attached) 

APPLICATION    

Available from the website address below.

Supported By.   Most recent annual report, accounts, bank statement, a copy of equal opportunities policy and job description if funding for cost of a post 

SPONSORED BY   

Lloyds TSB Foundation for England and Wales, PO Box 461563rd Floor4 St Dunstan's HillLondon  EC3R 8WQTel: 0870 411 1223Fax: 0870 411 1224

E-mail: guidelines@lloydstsbfoundations.org.uk

Website: http://www.lloydstsbfoundations.org.uk