There used to be a time in the UK that when there was a significant outage of a VOR a temporary NDB was located at the site, usually I recall on 669.5 khz.
One wonders why this has not been done on this occasion or is this because of an assumption that most a/c now have an area nav facility such as FMS etc?!
I don't think anyone could argue with a pilot asking for vectors under the heading of airmanship - as has been said above if in doubt ask.
However with the London TMA bristling with other facilities (many of them "static free") I find it surprising that anyone would have difficulty flying this SID with BPK off the air, given a little bit of pre-flight planning to anticipate the challenge. This is not to agree that a SID should be offered where a significant facility is u/s.
Or is there a concern here that if the SID is not quite flown precisely big brother is watching and one might get a violation but if you have asked for a vector it's on the tape?!