Doesn't this mean that one must either call them up for the QNH, or get their ATIS?
Yes - but what's the problem with dialling up the ATIS (if available) if you don't want to talk to them. There's plenty of VOR's as well as standard frequencies pushing out the Heathrow ATIS in the vicinity of the London TMA (for example).
And if there isn't one, as Evil J says - he'd like to hear from you. (If only to give you "Cleared to transit the XYZ zone, East of ABC, not above 1500'
)
(Worth pointing out here that one of the recommendations of the 'flyontrack' team was that the subject of RPS needs serious looking at, and even possibly abolishing, for the reasons that Evil J states. It isn't imposible to get a fairly accurate QNH wherever you are in the country - after all, it's not the biggest place in the world after all!)