Grants to help you grow your business

There is currently £6 billion of EU and Central government funding available to businesses in the UK today. One of my great frustrations is that most SME's don't consider themselves "the kind of company" that could access this funding. They are put off by the perceived complexity of getting the money, which plays into the hands of bigger businesses that have the resource to dedicate to the application process. Do any SME's have experience of applying for Grants and I'd be interested to know success and failure stories. Does the business plan part put you off?