There is a website
http://www.freebmd.org.uk/cgi/search.pl
which gives you free access to the index entries for the births, marriages and deaths in England and Wales since civil registration of these events started in September 1837. This is a great help indeed. The indexes are transcribed by volunteers and the task is by no means complete, so results get a bit patchy (not a criticism by any means! just an observation) around the time you have enquired about. It took me a while to work out the best way to use the site, and some knowledge of registration districts is helpful. For example, my parents, grandparents were born in Bristol, which was split over two counties (Gloucestershire and Somerset) and on a district basis you need to consider Clifton, Bristol, Bedminster, Barton Regis, Long Ashton as districts were rearranged and renamed. So it isn't always straightforward.
The other free site is
http://www.familysear...I.asp&clear_form=true
which holds the data from the International Genealogy Index (IGI for short), which can be helpful in tracing events before 1837. Not comprehensive, as it relies on first, the information surviving and being available, and second, Members of the Mormon church collecting and presenting the data, so thus is a secondary source. Useful at times.