Civil Registration of births, marriages and deaths (known as "Vital Records" in some countries) started on 1 July 1837 for England and Wales.
For further information see Civil Registration in England and Wales.
Here is a map showing the 1851 Registration Districts of Wales.. The Map is taken from The Religious census of 1851 : A Calendar of the returns relating to Wales, Vol 11, North Wales. Ed. by Ieuan Gwynedd Jones, UWP, 1981
The UK BMD web site "provides 2558 links to websites that offer on-line transcriptions of UK births, marriages, deaths and censuses. A wide range of other indexes and transcriptions are also available for most counties, these may include parish records, wills, monumental inscriptions etc. "
The Registration Districts appropriate to particular towns have been listed on a county basis.
Barbara Dixon has produced a very comprehensive description of birth, marriage and death certificates and each field to be found on them.