Great comments, chaps! It's good to see that I am not totally off my trolley.
I've come to a couple of conclusions:
1. I can't afford a new bike (really) and they aren't available anyway, so I'm sticking with the Amazon for the time being. It works, it's a nice ride, and I already own it. And I am very fond of it - for all the reasons kind people have outlined above.
2. I refurbed it in a hurry last year (and it's been a success) but that was only ever a 'proof of concept' thing. I spent the minimum money to see how it would turn out. Now it's healthy again I can tackle an upgrade programme properly. I sat and looked at it this afternoon with a couple of beers beside me and realised what it was all about. Everything these days is black. Black bars, black levers, black brakes, black rims. I am from an era where good components were polished alloy. Refurbing on the cheap meant everything was in
Halfords trendy black. It all works fine (ish) but it looks like a funeral.
So here is the plan: take every bit of the bike apart from the frame, and clean/refurb or replace as necessary, but only ever with alloy components. I've made a start by ordering some Shimano alloy cantilever brakes. Alloy levers next, and we take it from there. The original bars were in the blue/green speckled finish of the frame, and I am not putting those back on as they weigh a ton, so it'll be alloy there too. I've already refinished the stem in the original satin black, so that might stay. SJS Cycles look like a good source, but any other recommendations welcome.
I'm looking forward to this.