Lugo in Galicia, Spain, still has the original Roman walls around the center of the town. To go there you'd have to fly to either Coruña or Santiago de Compostela, which each have also quite a large medieval center.

I live in Dorset so preferably flying from Southampton or Bournemouth. However Heathrow or Gatwick aren't to difficult to get to. Thanks

There is actually nothing medieval about cobbled streets. In the middle ages the streets consisted of mud, feces and garbage. But let's not spoil the romantic imaginations...
Bergamo is, by the way, an excellent choice.
Also look into Swiss cities. The lucky Swiss kept themselves out of the devastating wars of the past two centuries, which means that all their cities have well-preserved centres.

Lyon is not what would immediately spring to mind, and I think it's a curious suggestion. Likewise Budapest. I would agree with Ghent, also a bunch of Dutch cities would fit the bill - Haarlem, Delft, Leiden.

I see you have direct flight from Southampton to Palma de Mallorca which is an amazing medieval city, but you must go there in the off-season(best in winter), because it's full of the worst kind of package tourists at any other time of the year.
I just returned from 5 days in Budapest and was not at all smitten by it. And it's not medieval. And as noted, neither are cobblestones.
I agree that Lyon is a curious choice, given the hundreds of possibilities.
Medieval hardly narrows down the number of places in Europe, though. Medieval is practically everywhere you look.
We fell in love with Bratislava. But Bergamo and Ghent are good possibilities, too.

I'm sure the regulars are quite fed up with me waxing poetic about Venice.
But they did basically stop building in about the 14th century. With a handful of exceptions.
Think of it this way: if you could reanimate the corpse of Marco Polo (1254-1324) and you dropped him off at the Venice train station, he could easily find his way home. And his home would still be there.
I second the Dubrovnik, Croatia comment. I also suggest Mostar, Bosnia & Herzegovina as well as Kotor, Montenegro. If you are curious if these are what you are looking for, I made a playlist of videos I shot during my experience there. Check it out! https://www.youtube.com/watch?v=dZiGMjX0poY&list=PLefDYkOKiLm3ygGW1rOGwPiZvvMPEjsWj
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