Prior to 1948, nearly all stamps were printed on watermarked paper as part of the security precautions of the time. The exceptions being some flat plate recess commemoratives issued between the wars. The reasons for these exceptions were that no suitably watermarked paper existed for the flat-plate presses.
Unwatermarked papers were introduced as policy, first in 1948, and revised again in 1956.
From 1948 on, stamps less than the current letter rate were printed on unwatermarked paper. This policy was intended for the general series only (definitives). Commemoratives: both the 1949 Lawson and the 1949 U.P.U commemoratives were also produced on unwatermarked paper while other's were not, making it rather nebulous.
In 1966 unwatermarked papers became standard for all values up to (and including) 2/6d.
During both periods, some definitives appeared on both watermarked and unwatermarked papers, simply because they were on issue for some years and consequently endured several print runs.