Michael Swan, Practical English Usage"used not to": formal style.
"didn㦙 use to" and
"didn īt used to": informal style.
The Collins COBUILD English Dictionary If something
used not to be done or
used not to be the case, it was not done in the past or was not the case in the past. The forms
"did not use to" and
"did not used to" are also found, especially in spoken English.
Quirk et al., A Comprehensive Grammar of the English Language"He
usen㦙 to smoke" and "He
used not to smoke" as preferred by many in British English," and "He
didn㦙 use to smoke" and "He
didn㦙 used to smoke" used by both British English and American English speakers.
L. B. Alexander, Longman English Grammar "used to" may be formed without the auxiliary "
do" as in "You
used not to smoke." But he adds that
didn㦙 is more commonly used to form negatives with
"used to". Alexander also states that "We can avoid the problem of the negative by using 𤉋ever�.� 𦴧red
never used to be so difficult.� "
Either the "formal" or "British"
"used not to" is fine, as is the "informal" or "American"
"didn㦙 use to" (or
"didn㦙 used to").
It īs also correct according to BBC Learning Service.
http://www.bbc.co.uk/worldservice/le...rnitv285.shtml 
