Looking at the link which Twix123 has kindly provided shows that a birth certificate is a valid (partial) proof of identity. There is nothing to say that it must be an original document. Indeed, there's a link to show you how to order a duplicate, so your birth certificate should be acceptable.
That link shows that you need to provide one additional document. With most of the examples shown the key factor seems to be that your National Insurance number should appear on the document. Income Support is provided through the Department of Work and Pensions (which is specifically mentioned in the link). If you look at the reference number(s) shown at the top of any letter relating to Income Support you'll almost certainly see your NI number quoted there. As long as it is, you've got sufficient proof of identity to obtain a driving licence.
Chris