1920s mystery girder frame bicycle - Royal Enfield or Robin Hood?

This machine has just come my way. I had been looking for a Royal Enfield Girder or Duplex frame for a while and then this appeared at the right price. Only thing is I really don't know what it is. To all intents and purposes it looks like a Royal Enfield but has no head badge and never has had. 

I've done some investigations and it seems that Robin Hood also offered a girder frame model, possibly actually built by Royal Enfield so this seems most likely what it is. The handlebars may just have been replaced some time in the bike's life and the Sturmey three speed dates from mid thirties but I would guess that the rest of the cycle is early twenties.

Some folks would restore it in this condition but I plan to oily rag and service. It's pretty much rideable as is, but lacks pedals. 

If anyone out there can recognise the manufacturer please do let me know.

Mid twenties girder frame cycle. 28 inch wheels.

Offside view.

The mudguards are very distinctive and may
give a clue for identification?

I like rust and this is a good coating of it. No structural
damage at all just a good patina.

Here's that all important girder. The chainwheel seems to be
generic and doesn't give any clues as to marque.

I'll even leave the period bodges in place if they work!

Perhaps the lamp bracket holds the key to identity?

French club rider 1908

Evocative photograph of a French uniformed club rider from 1908.

Bicycling Bee Gee and Lulu

Maurice Gibb from the Bee Gees and Lulu on a tandem in 1969.

Back when I worked at jack Hearne's cycle shop I remember him saying that one of the Gibb brothers took up cycling in the seventies as a diversion from the excesses of the pop industry. I cannot remember which of the brothers it was now and I've searched in vain for a picture of a Bee Gee on a Hearne cycle. Can anyone out there help?

Bee Gee Maurice Gibb and Lulu on a tandem.