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Mine has 27x 1&1/4" (630) wheels and currently is on 32mm tyres with mudguards, which is probably the limit. If you got one of similar vintage (1982 ish) and fitted it with 700c (622) wheels you could probably go substantially wider. You'd need some very long drop brakes though.
Edit: This listing shows a 700c conversion on the original brakes actually. Does look like there's lots of room for wider tyres though. https://www.ebay.co.uk/itm/295946627695?mkcid=16&mkevt=1&mkrid=711-127632-2357-0&ssspo=BfBE0sEeQrC&sssrc=4429486&ssuid=2oiWpP7gSxu&var=&widget_ver=artemis&media=COPY
What's the biggest tyre + guards combo you can get on these?