Indeed.
Essentially the crew were unable to navigate the aircraft on standby instruments (i.e., C172 style: HSI, altimeter, ASI). I would have never thought that could happen in a European B737 operation.
Judging the ATC actions from what is described in the report, and from personal experience elsewhere, I would say LHR was a great place to have this kind of problem--certainly I wouldn't want that to happen to anybody in, say, BCN.
the thing that amazes me most about this incident is the crew noticed the failure immediately after takeoff, but continued their climb into the 1500' cloudbase, instead of remaining VMC and declaring an emergency.
They did declare an emergency all right[*], and they attempted (not very skillfully though) to do what they are supposed to do, which is fly the departure. Commercial flying has very little in common with recreational flying (as illustrated by their inability to steer the ship using the good old steam gauges).
[*] Correction: They did not, actually, nor one was initiated by ATC. I misread part of the report.
Lastly, I have to disagree with your following comment:
A major disaster was narrowly averted
No it wasn't. A B737 getting lost is not anyone's idea of a good day out I wouldn't think, but your comment is sensationalist. According to the AAIB report, at no point was control of the aircraft compromised, merely its navigation.
Interesting report nonetheless.
