DWP provided the data they said was too hard.
I need to ask for how many national insurance numbers have been issued in total, but my best guess is about 135M since they were introduced in 1948. This figure obtained by summing population that year with live births since then and estimated annual immigration figures.
Per DWP,
- 1,673,313 people with duplicate full name and date of birth
- 33,274 of them could be differentiated by gender
These figures seem rather high, but the key point is that gender would be the disambiguating factor in fewer than 2% of cases, and is relevant for this purpose in approximately 0.025%.