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Lever position -
I was wondering about that as they are low but still in quite a good position.
I did initially think that the position was correct for the period but must have been the original owners preference.
SideshowBob-
Considering what a classy bike you have there, I doubt whether the original owner would have put the brake levers in that position because he would certainly have known that you don't just hold the bottom of the bars. I notice in you first photos of the bike the handlebar stem is too high (you seem to have corrected this) which suggests some one in the past didn't know how to set things up.
I think this frame has almost certainly been resprayed at some time in the past. I can't believe it came out of Gillott's shop with no transfers.
Incidentally, although the shop was in the South East, a lot of successful West London riders rode Gillott frames - Dave Stalker and Jeff Marshall being two examples. This was at least partly because Ron Brown worked for them. Ron (originally Calleva RC, later Hounslow & Dist) was a charismatic hard man (no pain, no gain!) who had lost an arm in childhood, but this didn't stop him being an excellent bike mechanic and a very strong rider. His idea of an Easter training weekend was: meet 2.30 am at the Travellers' Rest (West side of Hounslow) ride to Aberystwyth, and that would just be the Good Friday!
If you were a young guy riding with Ron, your obvious choice for a new frame would be a Gillott.
I've got a picture of him which I'll post shortly.
clubman
Oil
I can't see anything wrong with using ordinary car engine oil. Molybdenum disulphide (Molyslip) is a good additive, especially if you happen to ride in the rain since it takes longer to wash off that straight mineral oil.
You've certainly done a great job with the cleaning - it looks ready to ride in a BLRC race!
I shouldn't be surprised if you have the only Gnutti cranks in existence with their original chrome - even when I was young the only ones I saw had already started rusting.
One small point: the bike would look more 'gen' (as we used to say) if you move the brake levers further up the bend of the handlebars. It was intended that you would be able to use the brakes when holding the top of the lever hoods, as well as from the bottom of the bends.