I don't know if American English is sufficiently close to
British English to make this an accurate answer for you, but here's the
answer about syllabic N in American English. Hopefully, the two
varieties of English are the same in this particular respect.
The syllabic N occurs in American English only when the following conditions apply:
1. The syllable preceding the syllabic N is stressed; the syllabic N is unstressed.
2. The preceding sound is t or d.
3. The sound preceding the t or d is a (stressed) vowel OR a
(stressed) vowel followed by an r. (If we include all R-colored
vowels within the set of "vowels", we need only say in this condition
that a vowel precedes the t or d.)
So "Gordon", "Jordan", "garden", "Morton", "Martin", "Burton" all
contain syllabic N. (The t or d is preceded by a vowel (R-colored) in
each case.)
However, "wanton", "London", "Hampton", "Compton", and "Clinton" do not
contain syllabic N because the t or d is not preceded by a vowel, but
by "n" or "mp".
CJ