I decided to step back and think about this problem for awhile.
The thermal expansion coefficient of liquid gasoline is 0.095 percent per degree C.
The thermal expansion coefficient of vapor phase gasoline is 0.340 percent per degree C.
On a hot day, suppose it is 90F or 30C, with the engine at 190F or 90C.
For a difference in temperature of 60C from the tank to the engine, liquid will expand 5.7%, whereas vapor will expand 20.4%.
I believe vapor lock is a condition where liquid fuel is turning into vapor in the jet and the passage from the float bowl to the jet, and expanding according to the thermal coefficient, thus it is too lean, making the car difficult to start when hot. The reason liquid turns to vapor too soon is what is known as heat soak, excessive heat from the head getting to the carb body and then getting to the liquid.
If the heat is somewhat more severe, it will vaporize in the float bowl, and if even more severe, in the fuel pipe between the float bowl and the fuel pump; thus if the only vent for this volume of vapor is the jet as it passes the needle, the pump will not be able to push liquid fuel in, as it is vaporized too quickly and expands, effectively creating a back pressure.
In the most severe case, it vaporizes in the fuel pump. If the heat gets to the fuel pump and vaporizes the fuel, it cannot be pumped forward.
Heat transfer measured in Joules per second or Watts is directly proportional to the cross sectional area of the transferring medium, and inversely proportional to the thickness.
In our case the medium is the carb flange and body, including the studs nuts and washers. The gasket is thin enough to be considered negligible as an insulator.
Our fundamental root problem is that fuel is boiling in the jet and the supply passage from the float chamber. The ideal solution is to eliminate or reduce the heat transfer to the carbs.
Recirculating the fuel back to the tank only cools the fuel pump; it does not address the root problem of heat at the carbs.
We have one design advantage in that the radiator top tank and the water manifold are higher than the carbs, and the hottest coolant will migrate up away from the cylinder head. Possibly this may be the reason we do not hear of this problem often with our saloons. In the Model T era this was known as the thermosyphon system. XK120 did not have this advantage, the header tank being at the same height as the intake manifold.
Heat shields between the manifold and carbs have been tried on some other makes.
But our pushrod engines do not have an external manifold, so that solution is irrelevant for us.
Vent tubes were added to float bowls beginning with late Mark IV and then Mark V, which allows some of the vapor pressure to let off there as it expands, rather than only through the jet.
A remote fuel pump was used on Mark V and XK120.
Fiber insulator spacers were added to XK120 and Mark VII beginning in late 1952 with engines W.6919 and B.1752, and continued in use on all subsequent carburetor models. Unfortunately this change is not described in any factory issued Service Bulletin, but experience among XK120 owners has shown this to be an effective solution, and earlier 120s are often converted.
Switching on the starting carb sometimes will get a hot car started.
If vapor lock happens frequently, perhaps the water manifold is clogged with crud.
On the 3-1/2 Litre, one could make a phenolic fiber or Bakelite or high temperature plastic spacer the same thickness as the current C.347 aluminum spacer. Then the starting carb pipe would not need to be modified. Heat would still transfer through the studs, but their cross sectional area is much smaller than the flange, so the Watts transferred would be reduced.
On the 2-1/2 Litre there is no current spacer, so if spacers were made and added with longer studs, the starting carb pipe would have to be modified, either with 1/2” copper tubing or a rubber hose.
On both engines, vent tubes could be added on the float bowl tops.
A length of rubber hose between the fuel pump and float bowls is an effective heat insulator to stop heat transfer to the pump.