Most of our church records prior to 1961 are deposited at the London Metropolitan Archives 40 Northampton Road, London EC1R 0HB. See their information on this website. The churchyard is no longer used for burials. There is no known complete record of burials or tombstones or those buried in the crypt. However some monuments which existed in the former church (destroyed by fire 1841) are described in Allport's book (pub. 1841) which can be seen here. Later in the same book a few of the churchyard monuments are described here.
The population of Camberwell was growing very fast throughout the nineteenth century so unless you have very positive evidence that the birth or marriage took place in Camberwell, the chance of finding the information you require is somewhat remote. After 30th June 1837 the national register of births marriages and deaths began. These are held at the National Archives Centre at Kew. See http://www.nationalarchives.gov.uk .They are indexed quarterly so you need to know the quarter the event took place in. If you find the entry you can then request a copy certificate.
Birth Certificates give the mothers maiden name which baptism registers do not. Traditionally marriages took place in the bride's home church so a search of parish records where the couple subsequently lived may not be fruitful.
The National Archive site allows you to search the census records 1841, 1851, 1861, 1871 1891, 1901 and Births Marriages and Deaths from 1837.
If you are not able to do the research yourself you could enquire of the Society of Genealogists, 14 Charterhouse Buildings, London EC1M 7BA Tel: 020 7251 8799.
Most Southwark Public Libraries have a copy of Blanche's 'The Parish of Camberwell' published 1875 and reprinted by the Camberwell Society.
See also http://www.ancestry.co.uk a chargeable resource with very good indexes
This website also gives information on resources held at the London Metropolitan Archive and the Southwark Local Studies Library.