There’s a challenge (working out which ones you could reach by train, that is) that I could not resist!
I think the answer is 169, with most of the unreachable-by-rail maps being those for the Shetlands, Orkneys, Hebrides, and remoter parts of Scotland (principally in the Highlands, but also a few in the Southern Uplands and Borders). Sheet 95 is the Isle of Man, and 190 is the only one entirely in England with no rail connection (Bude & Clovelly).
So how long do you think it would take a reasonable person with a Gold Card? Not saying the man on the bicycle was unreasonable, just more motivated than most of us. A challenge for Geoff Marshall?