does physical size of lens affect light caught

At a given f no & same light conditions, does a larger physical diameter lens gather more light than a smaller one?

I am constantly amazed at how fast some people seem to be able to shoot compared to my typical exposures with Nikkor 80-400VR, 88mm dia f4/5.6. I know it is partly the light is awful here in the heart of England, I always drop the ISO when I get near the coast, also if it is East Anglia the lie of the land is flat and helps.

Also I think the actual hole in the body of a Nikon is smaller than that on a Canon; is this relevent?

At a given f/ number all lenses are the same. The f/ number is a function of the focal length (the f part) and the number is what fraction of the focal length would be. It nicely works out that, to similarly illuminate the sensor or film, the hole in the end where the light comes in has to be in the same proportion to the focal length.

If you consider a 200mm f/4 lens, then the hole in the front is 200/4=50mm and so on.

It follows from this, that the front of a fancy 300mm f/2 lens HAS to be at least 150mm diameter whereas a 300mm f/8 lens would only need to be 37.5mm diameter in order to accomodate the hole where the light gets in.

For a bigger diameter lens to give an advantage you would need to use it at a wider aperture than is available on the alternative smaller diameter lens. Stopping the fat lens down to the same f/ number as the thin lens makes them the same as far as light gathering ability is concerned.

The hole in the front of the camera isn't an issue (unless the hole gets smaller than the sensor or film). Nikon cameras have worked OK like that for years on 35mm film size and there are no DSLRs with sensors larger than old fashioned film.