You've also a right to ask how/where the information will be stored, the purpose for which it is required, and an assurance that the retention will be in accordance with the new data protection legislation that's about to land. Once they've satisfied those questions, particularly the latter, then I'd hand it across.
Of course, neither a passport or a birth certificate automatically indicative of your nationality or right to reside/work, so it's fair and reasonable to politely be asking the above questions.
Article 8 ECHR gives you a right to "private and family life, his home and his correspondence", subject to certain restrictions that are "in accordance with law", so a just and reasonable explanation for requiring sight of these documents is an utterly reasonable thing to request.