anything is singlespeedable given the right gearing and fitness, people have single speeded round the world :-)
there’s 3,800m (ish) metres of climbing so it’s not to be underestimated and the long long drags out from the valleys have destroyed people from The North who might be used to shorter sharper climbs
i’m a ride what gear you have single speeder so don’t ever change my gearing for a particular ride, if i wanted to do that i’d take my geared bike, but whatever gear you choose there will be steep sections you’ll probably have to walk (Amberley Mount, Washington, Saddlescombe) which will be about the same speed as riding anyway
your gravel bike will also be fine although you’ll miss the whoomfy comfort of mtb tyres and have to be a bit more wary of chalk gulleys and sharp flints