I don’t actually recall ever seeing a list of CAA approved sources, only advice that pilots are to ensure that the source is valid.
I have used that “App” for some years (still do although I no longer need it in an aviation context) and I know that many other commercial helicopter crews do because there is often no other method of obtaining up to date published met information so promptly, even at licensed airfields. I’ve never known it give incorrect information per se, although it may go “time out” if the mobile device can’t get a signal. It shows a warning if the data has expired. You haven’t mentioned if you have ever used any of the modern “Apps” in this way but each individual bulletin update is dated and timed.
I can’t think of a context where it would be so incorrect that it would be a causal factor in an accident.