This is the Willis World Clock in the London Science Museum.
I’ve not found out much about it, or who Willis was, but I did find a reference to a smaller versionin a 1939 copy of Flight magazine (here) and I presume the description is mostly valid for this version too:
The operation of this clock is extremely simple, with a twenty-four-hour moving disc in the centre and a separate minute hand below. The main face of the clock is laid out in sectors, with the names of all the more important countries and cities in the world indicated by arrows, and the time for each particular place is merely read cif against the appropriate arrow. The timing disc itself is clearly marked in a.m. and p.m. sections, so that, even when the twenty-four method of reading is not being used, there is no possibility of error. Those countries and cities where “summer time” arrangements are in force are printed separately in red type. For example, Great Britain and France have two positions, one at Greenwich time and one, for the summer season, on the mid-European time arrow.
Needless to say, such a clock will be useful in working out E.T.A.s which are likely to be at or near nightfall, and also for timing the reception of both weather broadcasts and others required for D/F bearings. The world clock is obtainable from J. H. Willis and Company, Ipswich Road, Norwich, and the aircraft or small marine type, for instrument-board mounting, is priced at 137s. 0d.
One of these – non-functioning, I think – was sold on eBay recently. You could have bought it for just £13.