Slammed Austin Somerset?

They are the last of the separate chassis Austins, but basic design of the front suspension is similar to the later cars including the MGB. However, I looked into fitting discs to my A55 Cambridge and, apparently, it can be done using MGB parts with some trick engineering of the kingpin/stub axle but it messes up the geometry. I've not had a problem with the servo-assisted drums, so haven't ventured any further.

^^^ That’s pretty much ‘bob-on’ what I was thinking when I saw the first image. A little like an early Karmann Ghia looking so cool on stock wheels lowered. 
Not sure what that would do to your turning circle, but just about perfect otherwise. 
I do like the swept line down the side of these. Would be good if you could do a little something to accentuate it slightly more, so you don’t have to depend on the light falling just right to draw it out. 
Littlepixel - you have skills!!!

Very narrow track, very high centre of gravity, handles like the Queen Mary.

Somersets are awkward to modify, which is why people generally don't. It's not impossible, they just don't like to make your life easy. Or so I'm told. This is second-hand knowledge so anyone that knows better please do correct me because I'd rather learn than work on assumptions. Here's what I've been told over the years:

Engine - MG B performance upgrades are where it's at. B series is a pretty versatile lump and well catered to.
Rear Axle - It's narrow for the size of the car and because of the rear arches, without modifying the arch opening, you have to keep it narrow. This also limits the size of the wheels you can put on because there's surprisingly little room at the back.
Suspension - woeful. Adequate for the time the car was built, and a big stumbling block for getting the best out of any performance upgrades. I expect it's easier to fix this side of things now since there's so much more aftermarket support available, what with the huge hot rod scene.
Steering - vague. Mostly down to worn out components and the fact it's a steering box, so theoretically this can be improved with modern or just new components.
Arches - there's not a lot of room in them. Enough for the wheels to do their thing in standard width but as soon as you start lowering or going to wider wheels, they quickly interfere with one another. Stepping down an inch on the steels is an option, though that can limit tyre options and smaller wheels can look a bit lost in the Somerset's arches.

I do wonder if channeling the body over the chassis slightly in addition to a modest suspension drop is the answer to the car looking low but remaining practical. It's a whole pile of work to do as these jobs always are, all depends how dedicated to the cause you're feeling. Roof chops really help the proportions (and that Enbloc's sister's car is a stunning example of that). I do wonder if spats/fender skirts would help visually lower or just make the Somerset look even more dumpy, if they do help lower it visually that's an easier option than chopping and channeling if less cool. Perhaps combine it with an exterior visor over the windscreen to add some horizontal to the profile and flatten out some of the chonk.

Could you not find a suitable more modern chassis and body swap?

Sort of like what Dez is doing with his jail bar?

Would a reliant SE be about the right dimensions?

Hold on. Quick bit of Googlefoo shows that the Somerset is 92” and the SE is 103” slight stretch in the front arches?

Or a Vittara is 87”

Mx5 has the right wheelbase but not a separate chassis.

Would be an interesting project.

P.

where is SOC when you need him

retrorides.proboards.com/thread/39982/mayday-thread-car?page=1

A VW beetle is about 95” and has separate chassis, lots of chassis kit stuff available - narrowed beams and air bags, but would be quite the project.
Especially as the engine would end up in the wrong place and cost a bit to get any performance to lug around the bigger body.

I hadn't

If it's just "kustom" style that you're after then maybe try and channel the body over the chassis, to get it properly low. That way you aren't messing up any goemetry and you won't be wanting wide wheels on that style of car anyway, or a fast motor for that matter.