Here's a useful database from Findmypast. If you can't find your ancestor on the 1871 census, could he have been serving overseas in the British Army? The 1871 Worldwide British Army Index is effectively a census surrogate which lists over 200,000 officers and men serving in Her Majesty's army. My old favourite, Edwin Mole, is there, serving as a private in the 14th (King's Hussars) who, at the time, were stationed at Cahir and Ballincollig in Ireland. Over 30,000 of these entries contain additional information such as date or year and place of birth. Well worth investigating if you have come up against a brick wall or two.