If the work required is voluminous then they do not have to provided it.
I was talking about this aspect of FOI with a writer/researcher. His view was that properly framed requests for specific information should get round the problem of the authorities refusing disclosure on these grounds. Once you had the initial information then the pointers for supplementary requests would become apparent. I am sure that many aspects of FOI will be thoroughly tested and explored over the coming months.
I can foresee a niche opportunity for FOI consultants specialising in drawing up disclosure requests.
YS