Mk2 - Front brake hydraulic hose fitting.

3/8 UNF

As Peter says, the Norton Lockheed master cylinder and caliper are 3/8"-24 UNF. (Although I did see a caliper on eBay recently which had been re-threaded to some oversize, presumably because the original has been stripped.)

What you put inbetween is up to you but the typical, single hose setup is a banjo at the master cylinder and a 'swivel' joint at the caliper. The caliper fitting then consists of a female hose-end that goes to a male-male adapter screwed into the caliper. The hose-end and adapter have a cone interface. The hose-end and adapter are paired where  thread and the 'sense', i.e. which part is the convex and which is concave, can vary but must match.

I have such a hose-end / adapter pair here, marked E104-3 A UK BSP. Convex hose-end, concave adapter.  And it probably is BSP. But the actual thread used doesn't matter so long as they're paired.

Hose itself is AN-3. Here's one that's probably the same as you're using: https://www.venhill.co.uk/e332-3ss-3-hose-end-90-degree-swivel-joint-stainless-e332-3ss.html

Search 1/8 BSP for all similar fittings.

The 3/8 24 UNF fittings are readily available, Goodridge made a good selection as they are used by the Mini restorers. Surprisingly, many industrial hose manufacturers stock them as they are Goodridge agents for the commercial size hoses. 

3/8" and M10 banjo unions are the same. Different bolt, obviously.

You don't say what vintage Trident but if it's Commando contemporary then it's also 3/8 UNF. Japanese tend to be M10x1.25, Brembo are M10x1.0. Note that 3/8 bolt will go into M10 female thread, M10 will not go into 3/8. Don't mix them up - it will end badly!

The hose is AN-3 and you want compression fittings to suit; these will not make reference to 1/8 BSP.

Ask Venhill, they'll tell you what you need. You can have either a complete, ready-made hose and fittings or the bits to make your own. https://www.venhill.co.uk/

Lockheed were quite early adopters of UNF.

The caliper has a parallel thread and as standard, the Bundy pipe flare forms the seat.

UNF threads on vehicle hose connectors of this era are usually associated with 45° SAE flare fittings. From memory, the original system uses this, with a conical "nose" on the male part and a convex seat in the female / nut.

Watch out for 37° JIC fittings (also UNF) and 30° JIS (Japanese) which combine BSP thread with a 30° seat.

Thanks to Richard for info on this (literally) vital topic.

It's a matter of concern that there should be such actual diversity in what can appear to be similar fittings in a safety-critical area.

Can anyone recommend a web-site that explains the issues clearly for non-specialists?

To return to the OP's observation that his brake hose has 1/8 BSP, presumably swivel, fittings at both ends, here's my explanation for those of us who've been happily making up hoses with compression fittings for years.

Venhill are pushing their pre-made Power Plus brake hoses which have swivel fittings on both ends and are then configured to go between the bike components (3/8 UNF master cylinder and caliper in our case), by the addition of screw-on banjos and and threaded adapters.

A swivel fitting is a useful device to take the twist out of the hose but you only need one per hose*. So why two? My guess is that it is to create a standardised hose that can be manufactured to pass TUV and DOT standards, essential if you want to sell in Germany, and then customise with appropriate ends. The OP's hose is Goodridge so presumably they have the same considerations.

It seems unlikely that Venhill would create yet another taper form but when asked they said : "They are unique to our hoses that we make up in the factory.". Therefore the only sure position is to use Venhill fittings with Venhill hose and Goodridge with Goodridge.

*In fact you don't need a swivel fitting at all if you have a length of steel pipe in the line since the nuts on that do the same job.