The cumulative number of officially-registered mosques in England and Wales is available here, collected from manuscripts held at the General Register Office.
Data on officially-registered places of worship are published in Marriage, Divorce and Adoption Statistics, Series FM2 (London: Office for National Statistics). The registers themselves are stored at the General Register Office, Smedley Hydro, Trafalgar Road, Birkdale, Southport, PR8 2HH.
These data were collected by Simon Naylor from the GRO’s Register of Places of Worship manuscript records, as part of the Leverhulme-funded project ‘Ethnicity and Cultural Landscapes’ (Leverhulme/F773), directed by Ceri Peach at the University of Oxford.
Note that not all mosques are officially-registered and exist privately, for example above business premises.
These figures are not given in proportion to either the total population or the Muslim population.
Mehmood Naqshbandi publishes estimates of the number of mosques in Britain, both registered and unregistered, via a mosque/masjid directory at his comprehensive and privately-run website Muslims in Britain.