You are all so amazingly helpful and generous with your time, advice and offers of tyres! What an amazing community I've stumbled across!
I am now sorted out with a set of sparkling (well they're really kind of matt but you know what I mean) new tyres that fit a treat. Yes they are 559 so I must have mis-measured (just tell tell my family that I got it wrong!).
I have now sorted the bike with new tyres, second hand shifters and brake lever assemblies, new inner and outer cables for gears and brakes coupled with a damn good clean and re-grease of the chain followed by adjustments of front and rear derailleurs from end shops to indexing. All this has transformed my old weary workhorse into a new machine....maybe I don't need need that shinny new Trek, Giant, etc after all...we'll see...
Many thanks again!
Oh yes what did I get? - I couldn't find stock of the Big Apples that many of you had recommended but I found a pair of Continental Double Fighter 26x1.9 at my local Halfords. A little hard to fit but the ride is great.