Two suggestions from me - firstly, a classic /vintage touring bike. It should come in well below budget, will do all that you want, and will last for a lifetime. I rode 70 miles yesterday on a 50 year old Peugeot AO-8 that has front and rear rack fixings, and a supremely comfortable ride quality.
Second suggestion is a Thorn - a Club Tourer would fit your requirements very well, although it would be slightly over budget.
I see a lot of Thorn bikes on Audax rides; they look very well built and the owners are invariably very positive about the bikes.
https://www.thorncycles.co.uk/bikes