Try a search, been done a few times, often in ATC Issues.
Short answer: "continue rwy heading" do just that, DON'T correct for wind, as separation from other aircraft may depand on you both flying specific divergent or parallel headings.
UK phraseology is now "climb straight ahead" to remove the confusion - this means fly rwy TRACK. Although it doesn't entirely remove the problem, as nicely demonstrated by a colleague during their readback recently "Roger climb straight ahead rwy heading".
