I think it would be a lovely getaway solo.
I've never been by myself but I've stayed in the hotel 4 times now - not only is it cheaper than the villas but it's so lovely. It's close to everything, the views are beautiful and it's always so clean. There's a small fridge so I tend to save pennies by bringing a few nice Tesco sandwiches along (not sure you're supposed to but still!) and goodies before I go. They've got a nice takeaway place if you haven't been before (the duck pizza's delicious and good value) so you don't always have to go out.
Like Tinks says the spa treatments or the spa 3 hour sessions are a great idea - I tend to do that by myself anyway when we go. Plus the scenery's lovely for quiet walks and you can pop into starbucks with a paper and stay for ages. Ooh I wish I could be there right now!
Of all the places I've been to I definitely think Elveden would be the holiday I'd choose if I was going away just me.