I’m a bit of a SDW obssessive. Not sure which way your BHF route takes you but going from Winchester to Eastbourne gives you a better chance of a tailwind.
I’ve done it quite a few times. It sounds obvious but try to do it as fast as you can otherwise it can be a long old day. There aren’t that many places to stop without heading off the the trail, so keep plenty to eat with you. I’m doing it on Saturday this week (and Wednesday next week as it happens) and I’ll be carrying half a dozen energy gels and a few cereal bars.
I also don’t like stuff on my back for 9-10 hours so I always use bottles and a large saddle pack.
Finally, not sure how your bike is set up. I normally do it on my cross bike because it offers me a lot of hand positions. You might want to think about bar ends just to give you a change now and again.