Afterwards I queried the W/V with the MetO, only to be told that the peak gusts had been well outside the limit! Thank for telling us, chaps... If in doubt, get the tower to pass constant W/V values on final approach.
Yes, absolutely. Unless things have changed radically, ATC and the Duty Pilot [if any] act as a cutout/liaison between Met and aircrew, and the Met folk provide ATC with routine obs and pre-agreed "specials". ATC will have/should have its own identical wind readout, but not the time trace {anemograph] that Met have. I think the current METAR coding allows recent peak gusts to be reported.
The thought occurs "does Met know the cross wind limits for each incoming aircraft ?" It certainly should, and the better SMetOs and SATCOs used to make sure that happened.