Yes. Banks like Monzo allow you to import your other bank accounts into their app. I did it for a while, but ultimately I found it easier to just have separate apps for each. Most apps are very good and improving all the time, so usually one isn’t much better than the other.
I haven’t looked for a one-app-to-rule-them-all, but in principle it’s possible.
I think the UK banking sector is in rude health. It’s very competitive and it’s easy to move. The quality of the apps is very much part of any competitive advantage.
I have accounts with four uk banks and it’s trivial to manage them. It’s an example of legislation working really well.