We have a Seat Ibiza, which would be a brilliant fit for your driving needs. Runs like a dream, great town car. Has a bigger boot than the Aygo.
My only gripes are that the acceleration is not amazing (but we do more long distance driving than you) - however, it can comfortably handle a motorway. And now we are a family of four, it’s getting a little snug - it’s not the kind of car to comfortably take pushchairs, bikes and so on.
I would advise going slightly bigger than you think you need, if you can afford it. Definitely Seat Ibiza/Ford Fiesta rather than Toyota Aygo. Our budget was similar to yours in 2018 and we ended up with a 2 year old Ibiza with about 22k miles on it for just under £7k.
We looked at the Toyota Yaris but boot was smaller, and also at Kia Rio but didn’t like it.