Hi Richard - Thomas Bigg was a grocer and lived in Lambeth. The Bigg family also were into the butchering trade and owned shops at one time. I am having difficulty in finding Thomas' father - (no info on LDS search results).
Have you been into 'FREE BMD' which only shows records from 1837-1904. The 1881 British census - also from the LDS site - gives a lot of information. Hope this is helpful.