A smartphone mainly for QR codes...

[Praktica]

Most of even the cheap smartphones should be quite capable of running the Covid app I would have thought.  Spend a couple hundred at least anyway otherwise the experience wont be great.  You might find if you buy a VERY cheap phone that with time you'll want to be able to do more with it and it's too low spec to be easily useable.

Worth noting; 

"The bitterness of poor quality remains long after the sweetness of the cheap price has been forgotten."

At Vodafone they didn't suggest any of their own branded phones. Some Chinese made phones can't access the Google store, where the app is found.