South Downs, UK: advice for a visitor

I'll be in London in April and I'll need to get in a long (30-40k) trail run while I'm there.

I was browsing AllTrails to get some ideas, and landed on the Seven Sisters coastal path between Eastbourne and Seaford - I figure if I do an out and back, it'll be a solid 40 and the views will be unbeatable.

Seems like there are a fair amount of places to stop along the way to refill water, etc (pubs and so forth) - any suggestions as far as that goes?

As for logistics - any thoughts on whether it's better to start at Eastbourne or Seaford, or if it makes a difference at all since I'll be going out and back. I was thinking Eastbourne simply because it'll be a direct train instead of a connection. I know Seaford->Eastbourne has more/better views, but I figure I'll see those on the way back, so...

Also - I'm used to having my car as a home base/storage space when I travel for a long run. I feel like I'll want a change of clothes before the ride home, if not for myself, then for the benefit of the people around me! I don't suppose there are any lockers at the train station - here in Canada, all that disappeared after 9/11. I found an app called Stasher that seems to list a few places that'll take your bag in for a small fee - any other suggestions?

In a similar vein, it seems that there are showers at the Eastbourne beach- is this correct? Will they be open in April? For that matter, will many facilities be open at that time of year as it's not prime beach season yet?

Last question (I think) - any other suggestions for other scenic trail running routes anywhere between 30-40km and within 2 hours of London? Mostly as a contingency in case of poor weather- I'm not afraid of rain, but I wouldn't want to be out on coastal cliffs in high winds or a storm.

Appreciate any insight! Thanks!