That phrase is not in the US Pilot/Controller Glossary, so the UK CAPs are "new information" for US pilots.
From FAA Order 8260.46C, Departure Procedure Program, page 10, par. 10.g(4):
g. Terminology. The following terminology should be used for initial climb instructions:
"(4) Do not use the terminology "Climb straight ahead…" or "Maintain runway
track...," as there is no guidance or reference definition of this phraseology for the pilot to apply."