Chester seems to have started as a registration district in 1870.
Concerning your suggestion of methodist chapels, I ran a test on Free BMD in Cheshire for the years 1859-1863 (99% covered by Free BMD). I used an english name, John Smith, and a welsh one David Jones.
Out of 111 John Smiths, two registrations were in Wrexham. Out of 35 David Jones, 25 were in Wrexham.

Note to Joan Lee:
If you do decide to get a birth certificate, I suggest that you get Martha's, rather than Margaret's, as the FreeBMD coverage in 1857 is well below the 99% in 1862.