Hi Caroline,

The world is your oyster on the used market for €20,000. Using the Carzone search filters with that upper limit and an automatic gearbox threw up some interesting options that might work, depending on how new you were looking, or whether you'd consider an electric car. 

Ones to look at:

Honda Jazz

Kia Soul

Nissan Juke or Qashqai

Suzuki Ignis

Toyota C-HR

There are loads more to choose from, but all of those are easy to get in and out of, in budget and available with an automatic gearbox. They should all be reliable, too.