My mom is 76 and I gave her a 6" Nook Glowlight 3 and she loves it. Larger screens are nice, but don't think 6" won't agree with old eyes, especially if cost is a consideration.
Why not look for an older Kobo? The models listed below all have lighted screens, sleep covers and work with Overdrive in the UK (thank you for mentioning location. It makes it SO much easier!).
Except for the Nia, these are all older model Kobos that have been replaced by newer models. You should be able to find these used on eBay for a reasonable price:
- Kobo Nia
- Kobo Aura edition 2
- Kobo Clara HD
- Kobo Aura H2O edition 2
- Kobo Libra H2O