Brian Barder, who has provided unfailing interest in and support for my Guide to English Language Usage, objects strongly to my recommendation of I didn't use to play football as the negative form of used to, and that he would seize the alternative form I used not to play football with both hands. What is there to say about this?
My reasoning in making this recommendation is that use pronounced /ju:s/, i.e. with an unvoiced final consonant, is an auxiliary verb which, not being a modal verb, takes the infinitive with to. Thus I see it as analogous to want. I used to play football has the same structure as I wanted to play football. This being the case, it follows that the negative form must be I didn't use to play football and also that the question form must be Did you use to play football?
As for the form I used not to play football I see nothing to recommend it, though I recognise that it is widespread. The use of an auxiliary verb without do is restricted to modal and semi-modal verbs, and is followed by the bare infinitive: I won’t play football; I needn’t play football. As there is no obvious reason why the negation should not be transferred, and this is not a case of predicate negation, I can see no grammatical justification for the latter form.
Why then do people prefer the form without do support? I suspect that we are dealing with that old and curious phenomenon, hypercorrection. The clearly incorrect form *I didn't used to play football is sometimes found in print. In speech this cannot be distinguished from I didn't use to play football and people who wish to make it quite clear that they are shunning a solecism can only do so by avoiding the homophony completely and using an alternative form.
Fowler isn’t much help; under use 2 (e) Burchfield tells us that the negative form without do support is found ‘only in very informal contexts’ but he fails to recognise any distinction in do support between didn’t use to and didn’t used to. The Comprehensive Grammar of the English Language (Quirk et al. 3.44) gives He usen’t [sic] to smoke and He used not to smoke as British and He didn’t use to smoke and He didn’t used to smoke as both British and American. It adds ‘The construction did … use to is preferred to other constructions in both AmE and BrE. The spelling did … used to, however, is often regarded as nonstandard.’ This book was my main reference for grammar and my recommendation for non-native speakers is a simplified version of its comments. The Cambridge Grammar of the English Language (Huddleston & Pullum, 115), which was not available when I wrote this article, shows He usedn’t to like it and Used he to live alone?, both marked as ‘grammatical in some dialect(s) only’, and He didn’t use to like it and Did he use to live alone as unmarked forms. It mentions that ‘choice between the negative variants is sometimes avoided in informal style by using never: He never used to like it.’ This bears out my recommendation.
I might add too that the tag question for used to is naturally made with do: You used to play football, didn’t you? Does anyone really say usedn’t you?
Finally, I would point out that my book is intended to make recommendations for non-native speakers, so I tend to go for the simplest solution whenever possible.