You're not supposed to drive 60mph on those tiny roads.
Why are they 60mph? Well, the symbol they display doesn't say 60mph, it's basically just a slash symbol - it should be read "National Limit Applies" or perhaps "Derestricted" and it so happens that the law in the UK says that if there's no other rule in place that limit is 60mph and on these tiny roads nobody has put in place a more specific limit so that's the law.
[If there is carriageway separation, e.g. a larger road on which traffic flowing in the opposite direction isn't sharing the same tarmac, this global rule says 70mph, but no tiny roads have multiple carriageways, actually sometimes it feels like there's barely room for one let alone two]
However, just because there isn't a lower limit doesn't mean it's appropriate to drive at 60mph and people who do are generally maniacs. Where I grew up there are lots of these roads, steep, winding, narrow tracks paved in the 19th or 20th centuries for access to a farm here or a cottage there, and maintained by the public. You absolutely might turn a corner and find an entire flock of sheep in the road going "Baa!". If you're doing 60mph after you've killed a bunch of sheep and the bodies start smashing through your windscreen you're probably dead. Sheep don't have lights, don't know about jaywalking laws (which Britain doesn't have anyway) and aren't smart enough to have considered this risk, they're just there and now you're dead. So you drive at maybe 30-40mph on the straight parts, slower on curves and always pay a lot of attention 'cos things can go very bad, very quickly.
Roundabouts are a bit different. The UK has a lot of what are called "mini roundabouts". As a pedestrian, or perhaps on a bicycle these do just look like they're small roundabouts, too small for the island in the middle to have any purpose so it's just paint. But in a vehicle it's apparent that the island can't exist because you'd crash into it, perhaps not in a Mini but certainly in a bin truck or a bus. The mini roundabout isn't a roundabout except in the sense that the same rules apply as if it was, which means if I can see you can't enter before I do then I know you mustn't enter, I have right of way, which means I needn't slow down - you won't be in my way, you're not entering.