I've never heard this phrase as such, but I wonder if pike is short for turnpike? A turnpike was a main road maintained by tolls charged to the users (I think 18th and 19th centuries). The toll-houses can occasionally still be seen beside many British main roads. Sometimes the list of charges survives -- for example there is a good one on the famous bridge at Ironbridge.
If I'm right, your phrase would just mean "coming down the main road" -- perhaps from a town some distance away.
I think the origin of the word turnpike is that the toll-gate would originally be a pike (an axe on a pole) hinged across the road.
Now then -- those vultures were American, weren't they? (At least, the lyrics presumably would have been, even if the accents were supposed to be Liverpool).
This gives me a feeling that Americans still use the word turnpike. Perhaps it's equivalent to the British A-road? Any Americans out there?
Back in the 1800's logging was huge in Canada, still is but back then the easiest way to transport a huge&nb sp;amount of cut down trees was to float them down streams or rivers. These waterways were called pikes. I don't know if Pike was slang or if it means like, a straight passageway or something but from where I'm from, I just assumed that it got it's origin from that.
For New Foster (you cheeky monkey) I'm close enough to our fine american friends to know that if you wanted to ask, what is the quickest way to the Louisanna Turnpike, ;one would not say "How do I get to the pike?", if that is what you wanted to know. They do still use roads called turnpikes but their major highways are called "Inter-State" highways.