There's a little strip called Prestwick 20 miles up the road....
A good historic background to Turnberry is
here.
According to
this site, (which is not an official source) it's not got an ICAO ident, but isn't shown as closed.
Unfortunately, the gash charts that I have at work with me have a gap between Liverpool and Prestwick (and Turnberry's just off the bottom!), I don't have my Pooleys in work with me, so I can't see whether it's shown as an active airfield.
From the various Web sources I've looked at, I believe that it's probably disused (overgrown by golfers
) and may just be farm strip if anything.