Za Rodino seems to have hit the nail on the head. Most countries maintained full diplomatic relations with Switzerland, Portugal and Spain throughout the war.

In the case of Vichy France, nations including Canada, Australia and the US held full diplomatic relations until at least the end of November 1942 when German forces moved to occupy much of Vichy territory in the south of France.

The key for the British appears to be Canada. Although diplomatic relations between Vichy France and Britain collapsed after the Royal Navy's destruction of the French fleet in Algeria in 1940, Britain encouraged Canada to maintain full diplomatic relations to keep a communication channel open with the French and others.

It would therefore be relatively easy for the British personnel, diplomats, secret service etc - and perhaps civilians - to travel to Lisbon by BOAC, then through neutral Spain, into "neutral" Vichy France and across the Vichy France border with Switzerland, all under Canadian passports supplied by Canada, Britain's Commonwealth territory.

However, there appears to be little commercial aviation involved. It seems Switzerland's only carrier at the time Swissair suspended all commercial flights during WWII, Iberia Airlines of Spain operated at most a domestic service and Air France had relocated to Casablanca in Morroco. The last commercial link between the Allied countries and Europe appears to be BOAC to Lisbon.