There is a difference between withdrawing a trade privilege which is being exercised, and not granting a trade privilege which is being sought.
Buster CT1K, the GATS does cover Air Services--indeed, there is an Annex on Air Transport Services. It's invocation would depend upon whether Singapore were to take regulatory action against one service supplier by denying traffic rights (in which case the GATS annex does not apply) or against one country's carriers (in which case it would).
If Singapore made the mistake of acting against BA alone, however, they would be in no position to squawk if the UK were then to take action against SQ by, for example, taking away their landing slots at LHR.
SATS would probably lobby the Singapore government fairly heavily against such action--both BKK and KLL are available as transit points from UK to OZ, and SATS would be most reluctant to see traffic bled off to competing ports.
SQ are also probably wise enough to recognize that they stand to lose fare more than they gain in such an exercise.