The 1881 Census obviously acts as a reference point.

1801: The work of Martin Ecclestone with the International genealogical Index (IGI) provides another reference point for each English county. See Statistics and the IGI.

1837: Possible reference point using an extension of Donovan Murrell's method for estimating the current population:

    Take the current estimation, and deduct from this figure the difference between all the births and deaths recorded since 1837.
    That is, 4 225 estimated today less (8 000 births - 5 000 deaths) = 1 225 estimated alive in 1837.

Post 1837, name populations can be estimated by adding together the birth and death registrations, dividing by the total equivalent registrations, and multiplying by the national population.
(b+d/B +D) * YearPop
It is best to do this for a range of years (say 10) and then to average the results. It may be necessary to factor in under-registration of births pre-1875.

Clive Essery has written a process which, taking the 1881 Census figures as a base, adjusts for each birth, death and marriage, to provide estimates for every year up to the present - as long as you have the GRO data:

All Births and adoptions Add 1
All Deaths Subtract 1
All Marriages of Males Add 1
All Marriages of Females Subtract 1
All Marriages of Unknown Sex Add 0

Clive details on his site possible causes of any errors:

  • Recordless name changes,
  • Immigration/Emigration unaccounted for,
  • Common law marriages,
  • GRO data errors,
  • 1881 Census transcription errors.

And some interesting Excel graphs

See Clive Essery, Counting your population.

A further refinement would be to compare the birth rate of your name against that of the national crude birth rate.