I suppose you could regard “nought” as a side-track in this discussion, but I added it for the sake of completeness because nought and nocht are related. Dictionary of Scots Language on nocht:
DSL - DOST Nocht, Noucht, Noght, Nought, Noch, Nouch, n. and adv. Also: nochte, noht(t, noct(h, noyht; nowcht; noche, nogh; nowt; noth(t, nothe, nouth(t; noʒt.
[ME. noht, noʒt, noght, nouʒt, nouht, ME. and e.m.E. nought, ME. noh (13th c.), nogh (14 c.), ME. (12–13th c.) and e.m.E. nout, early ME. also nowiht, OE. nóht, nówiht: cf. Naucht adv., No adv.3, and Not adv. and n.]
In certain instances some of the forms exemplified below, esp. nocht, no doubt represent editorial expansions of MS. abbreviated forms, of which not is much the commonest.
Nought, nothing; not.
Where the verb can be either trans. or intrans. and there is no other direct object, it may be uncertain whether nocht is to be taken as the noun (i.e. the direct object) or the adv.: see e.g. 1 (2) below, and examples with verbs such as Avail v. 1 (a), Care v. 1, Cure v.1 2 b, Dow v.1 1, Help v. 3 b, Mak v. 19 a, etc.
The citation shows that 13th century Middle English pronunciation was “noh”.
Interestingly, Alex Salmond, leader of the political party advocating Scottish independence, pronounces “not” with a “T”. Here’s one example - you need only watch about twenty seconds to hear his pronunciation.
edit: I sometimes say “nowt”, though always informally to other northerners.