syllable-initial (love that word) t-glottalisation. Also, on television, I heard somebody say nʌɪnʔɪjn nineteen. Where does this occur? The speaker didn't sound as if he artificially tried to sound folksy.
I don’t think anyone ever says *ʔiː for tea, *ˈʔɑːɡɪʔ for target, or *ʔreɪn for train, do they?
The best I can think of as slightly a less implausible candidate for down-market word-initial t-glottalling would be somethinɡ like ?ˈsiː jə ʔəˈmɒrə see you tomorrow. Has anyone ever heard that?
It’s not much different for word-internal, putatively syllable-initial t-glottalling. I don’t think anyone ever says *əˈʔæk for attack or *rɪˈʔɜːn for return (do they?). On the other hand I think I have heard ɡɪˈʔɑː for guitar, while ʔeɪʔiːn for eighteen (adjust the vowel qualities to please) is indeed widespread among the kind of speakers who use a glottal stop in words such as water and city.
Two of the teen numerals are obviously irregular: thirteen and fifteen do not fit the pattern of fourteen, sixteen, seventeen and nineteen.
The missing one, eighteen, is also irregular for RP speakers and many others, since it has single t, thus ˌeɪˈtiːn, despite the two ts of its transparent morphology (eight eɪt plus teen tiːn). On the other hand some speakers/accents, both British and American, have regularized the position by pronouncing it ˌeɪtˈtiːn.
(The teen numerals are all lexically double-stressed, and therefore susceptible to ‘stress shift’ in running speech. Let’s not get sidetracked into discussion of stress patterns, which is a different issue.)
The first t in this ˌeɪtˈtiːn is an obvious candidate for glottalling, just as the first t in nighttime. I suppose that if you manipulate the usual rule ordering so as to do glottal replacement before double consonant simplification you could explain the possibility of ˌeɪʔˈiːn. However, this would involve ordering a postlexical rule (glottalling) before a lexical rule (simplification), which cannot be right.
But then again there are speakers who have double tt (possibly realized as ʔt) in thirteen and fourteen. And, as you would then expect, there are some who reduce this cluster to a simple ʔ, giving ˌθɜːʔˈiːn, ˌfɔːʔˈiːn.
And, as Lipman noted, this can extend to nineteen, too. As well as ˌnaɪnˈtiːn, we can get ˌnaɪntˈtiːn ~ ˌnaɪnʔˈtiːn and even ˌnaɪnʔˈiːn.
With double tt ~ ʔt or bare ʔ I think you usually get pre-fortis clipping of the sonorant part of the first syllable (eɪ, ɜː, ɔː, aɪn), which might be taken to imply that there has been resyllabification, giving a fortis consonant as the coda of the first syllable, thus ˌeɪʔˈiːn, ˌnaɪnʔˈiːn etc.
I’m really not sure how to explain all this.