This series of posts will concentrate on why you may not be able to find a given person’s birth record. By that, I include not just birth certificates, but also baptism or christening records, family Bibles, and newspaper announcements of births. Only as a last resort would I accept a census record as proof of birth, not least because precise dates of birth are not given in census returns.
So, first reason you can’t find that birth? The name you know your ancestor by is not the one on the birth certificate.
Have a look at this series of entries. These all relate to my 2nd-great grandfather, but what conclusion would you reach as to his actual name? I generally accept the earliest known document as the correct name, with other names as alternates, but in this case should I put a different name? Feel free to give me feedback on this.
The earliest known record is the baptism register from 1835, where the father’s 
occupation is given as a publican. And, of course, this was before civil registration began in 1837, so in terms of the date, this is as close as I am going to get.
Next, the census entries for 1841, 1851, and 1861, each of which gives a different name. I find the 1861 census to be the most interesting, given the way the enumerator went about recording the names.
1841 census: 
1851 census: 
1861 census: 
And finally, his marriage entry. 
So, what conclusions would you draw about his name? Note that there are small details interwoven between the various documents, such as the occupation of his father, or the fact that his maternal grandmother is listed in the 1841 and 1851 censuses, which help to paint a more detailed picture.
Whatever conclusion you reach about this man’s correct name, I think you will agree that if I had restricted my searches to the name on the marriage certificate, I likely would not have found the other records, except maybe the baptism record.
Family History research in England 