Having now spent some time searching online and seeing how much variety there is out there, I’ve narrowed my choices down a little further by deciding to focus on European bikes.

Not the UK? – There have been some fine bikes coming out of the UK, but have to say there’s nothing I’ve seen that sets my heart racing.
I’ve seen some beautiful Italian (Chesini, Rossini) & French bikes (Bernard Carré, Limongi) – sadly none in my size so far – but the UK just generate an indifferent shrug.

Think of it in terms of old cars – Italy has the stylish sporty Ferraris/Maseratis, France has the quirky & often innovative old Citroens or Bugattis, while the UK is giving me an Austin Allegro or Ford Anglia. (Ok, yes I know the UK can also give me an Aston Martin, but I’m not seeing any in my bike search!)

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(For the car lovers, above pictures came from Honest John Classics site, where there are many others)

I’m sure if anyone ever gets round to reading this there may be fierce disagreement, but this is my opinion and my search – I will defend your right to have your own opinion (even if that is wrong in this case 😉) but beauty is in the eye of the beholder and my eyes find beauty in Italy.
Besides, in my warped logic, I’d rather have a bike that’s seen it’s fair share of sunshine & not had to endure our miserable weather.

With that in mind, I’ve cast my search a little wider into some of the local European sites – eBay is (mostly) easy, as you just need to check the “Worldwide” option in search item location (although, I still seem to see more if I search directly on eBay.it & eBay.fr – see postscript below).
Then there are the Local Ads/Gumtree equivalents in Europe – if you’re comfortable with these, there’s quite a bit of variety. If  your browser supports it (directly or via a plug-in), you could use automatic translation functionality which comes in handy here.
However – searching for “vintage steel bike frame” on an Italian site is not going to give you many, if any, results – you need to use the local equivalents and look in the cycling categories (although “vintage” and “Eroica” seem to be universally popular). I’ve put some of the sites/terms I’m having success with below, there are other word variations I’m sure you can use depending what you want

Country	Site(s)	Category	Frame	Vintage	Steel
France	Leboncoin	Velos	Cadre	Ancien	Acier
Italy	Subito	Biciclette	Telaio	Eroica, Epoca	Acciaio
Netherlands	Markplaats	Fietsen,Racefietsen		Klassieke	Staal
Belgium	2dehands	Use French or Dutch options

Just add or change word options depending what you are looking for
e.g.

Add “Acier” to a French search of  “Cadre Ancien” to narrow the results down to old steel frames.

On eBay you can chain the words together with brackets, to make a catch-all search across your target countries (sadly eBay in their infinite wisdom removed the ability to do wild-card searches a few years ago now)
e.g.

(cadre, telaio, cuadro, rahmen,frame, frameset, bike, bici, cycle, bicycle) (epoca, eroica, ancien, acciaio, vintage, classic, retro, columbus, vitus)

The eagle-eyed linguists will notice Spanish & German in there as well as a couple of frame material types that I’ve found appearing often in the results.

If I find something I’m serious about in any of the local European searches, my wife will be more than happy for us to have a weekend to collect – Yorkshire may be beautiful and full of many great bike shops, but I’m afraid it doesn’t have the same appeal (see “miserable weather” comment above 😄).

While this searching is returning a lot of lovely bikes it’s no substitute for seeing and touching, so it’s time to go on a field trip and get some hands on experience ☺️

Postscript:
Now my search is (mostly) completed, I thought I’d come back and provide a small update – it turns out that some local eBay sites actually have Vintage Cycling categories underneath the main Cycling category that we don’t have in the UK, so if searching within a specific bike component category – e.g. “Bike Frames” –  you may not see all the results from those local sites, as the parts you’re looking for may have been listed under the Vintage Component/Parts category.
To get around this, search at the higher Cycling category level and use a catch-all search string for the component you want, as per my frame example above.