A solicitor is a data controller for the purposes of the act and so is subject to the act. The act however covers "personal data" held by the data controller, I would think that in relation to a solicitor this would cover information like name address pps number occupation marriage details, that sort of thing. You would have the right to ask the solicitor what personal data they held and the right to have it corrected if it were wrong, the information held can only be use for the purpose for which it was given and the information must not be retained longer than is necessary.
The act does not give you the right to see documentation or correspondence which does not relate to you or which is covered by client confidentiality