Background checks by employer

I am currently working through an agency for a multinational and going for an interview for a permanent job with another multinational. I have just seen that they say they will conduct 'background checks'. I have no worries about past employers, qualifications, criminal record, credit record, etc. ( not even sure they would look into them), but I did not tell the company I am going for an interview with that I work through an agency. I'm just worried that if I do get an offer, they will contact the HR department of the company I am working through an agency for and be told there is no record of me there ( It is a very big company and I am not on the payroll of the company, the company pays the agency who pay me). Does anyone know what these 'background checks' actually entail , and should I tell them now about the agency, or just carry on and hope they don't go the company I work though the agency for for details?

Usually potential employers won't contact your current employer without your permission. Have they asked you for details of who to contact etc for references?