EU citizen living in the UK and moving to Berlin: UK bank accounts

As EU citizen, you will have no formal problems moving to Berlin.
Regarding your UK bank accounts and whether you can keep them without UK address, you better ask on the UK forum, not here!

Like Beppi mentioned, the question about UK banks is best posted on the UK page. But with Brexit so much up in the air who can say what the rules will be. Maybe Brexit doesn't even happen. I can imagine banks have planned out a couple of possible scenarios to fit to different outcomes but any certainty is impossible at this point. But why don't you ask your bank! Who would know better than them?

I really don''t understand some of the questions here sometimes. Why do people speculate or ask opinions on a forum rather than the people  or organization involved?

With regards to retaining your UK bank account; I kept my account with what is now HSBC open for the 15 years I lived in Germany, but it was >20 years ago and things may have changed; I do recall reading that some banks will make a decision based on your circumstances and why you need to keep an account open if you are leaving the country; receipt of a UK pension was deemed as being one of the reasons they would permit the account to remain open; bottom line though is it's probably best to ask your bank.