Main RDS tripping with lightning

[ban-all-sheds]

1. Having no real reason to assume the earth pin is not connected to the house system

You have that AAF - with something as vital as this you must adopt the position that right now you have no real reason to assume the earth rod is connected to your installation.

leaves me with the way ahead for my original problem of trip-outs. Perhaps I should go ahead with the fitting of an S type RCD of 300mA instead of the present 100mA unit and see if that helps?

NO!

1) You already have inadequate RCD protection - making it worse would be illegal.

2) RCDs like that are not cheap.

3) Substituting components in the hope that you'll fix a problem is a flawed approach, you need to do (or have done) a proper investigation to find out what the root cause is.

2. Is there some way of testing the earth pin connection integrity with my simple multimeter or is something more sophisticated required.

The latter.