Wot's this car bit called?

Not sure. Some cars have something like you described - but rather bigger - to control the anti-lock braking.

Union e.g. 3 way union, 4 way union

I'd probably call them a Henley block!

Bob Eager expressed precisely :

A brake manifold.

thats what I would call it

Same here - if you do a Google image search for "brake line manifold" you might see a picture of something you like.

However ... on cars with dual circuit hydralics, some of these manifold blocks have a balance valve thingy which will trigger a warning light on the dash if theres a leak in the system.

When you fix the leak you have to manually reset the valve. So dont throw it out (yet) - its probably not broken

Generally called a 3 or 4 way female connector. But they tend to be a T or whatever little bigger than the pipe union. If larger, may include a restrictor valve for front/rear brake balance.

MOT failure

I think that would be a hydraulic distributor, possibly with spool valves

I'd go with that

just like a central heating manifold

Single point of failure?

That's always the loose nut behind the steering wheel.

photo may help

Some cars have a separate "brake proportioning valve". This limits the brake pressure to the rear wheels.

On some cars (French?) it a load sensitive valve with a link to the rear anti roll bar.

Others (Japanese?) it's on the side of the master cylinder.

I had one fitted to the rear anti-roll bar on a Fiat 124 - I believe they called it a "tipping valve"

Ditto Astra 'F' Estate, but connected to the rear torsion bar which is also an anti-roll bar.