Adrian Morgan pointed out to me a Usenet comment in which someone says of some course of action that it "can hardly be a sane policy for anyone who is not evincing signs of heading distinctly dagenham". In this context dagenham is apparently to be taken as a synonym for "insane", by a rather devious etymological route. Dagenham is a town in Essex, England. On the District Line of the London Underground, Dagenham is three stops beyond the town of Barking (after Barking are Upney, Becontree, Dagenham Heathway, and Dagenham East). To be barking mad is to be crazy; and being dagenham is therefore being three steps beyond barking. The allegation of being beyond barking was leveled at Prime Minister Margaret Thatcher, according to this page at phrases.org. And this list of British idioms says a parallel use is made of the place name Becontree (two stops beyond Barking on the District Line).
So much for the etymology. Now for the syntax. Is it actually grammatical to say someone is "heading dagenham" (whether distinctly or not), under that interpretation of what dagenham means? I would agree with Adrian that it is not quite grammatical. Not too far out there beyond the boundary of the normal, but definitely somewhere out there. But why?
Well, the thing about the verb head is that it takes an obligatory complement, and demands that the complement should be a preposition phrase. You can't say *Let's just get into the car and head. You have to head into town, or head out of town, or head in some direction or other. It's a syntactic requirement to have a directional preposition phrase complement. In fact, the fact that you can say Let's head south is part of the evidence adduced in The Cambridge Grammar of the English Language (CGEL; chapter 7) that words like south should be regarded as prepositions that don't take noun phrase complements.
There are lots of other prepositions that don't take noun phrase complements: out, up, in, through, back, away, home, etc. Some of them (like up and in and through) can optionally be followed by noun phrases. Others (like away and home and back) never are. There are also plenty of other tests for prepositionhood that they pass; again, see CGEL.
CGEL also treats a class of words ending in -ward(s) as prepositions, for similar reasons. You can head homeward, or northward, or downward. If -ward(s) is fully productive, it should therefore be possible to say Let's head Dagenhamwards. But not *Let's head Dagenham, because Dagenham is definitely not any kind of a preposition, it's a proper noun.
So, Adrian and I both think, to say *heading distinctly dagenham is heading distinctly away from being grammatical in Standard English, though it's close that you can follow the drift if you pick up on the fact that Dagenham is three stops beyond Barking and thus dagenham means three steps round the twist or, in other words, cuckoo, crazy, insane, loopy, mad, deranged, nuts, loony, bonkers, gaga, out of one's gourd, out to lunch, off one's trolley, round the bend… (British English has so many words for mental illness and defectiveness that if lexical profusion were a sign of cultural importance you would think Britain was a nation of psychiatrists rather than shopkeepers.)
Heading round the bend is of course perfectly grammatical: although the complement round the bend is intended with the idiomatic meaning "insane", nonetheless round is a directional preposition, so the phrase satisfies the syntactic requirement that the verb head imposes. Heading for Dagenham also meets the requirement (this use of then preposition for is directional). But *heading dagenham does not. So that would be an explanation of why it sounds just a little beyond the syntactic fringe.