Planning to retake English language test for PhD admissions in the UK, but listed previous average in my CV - should I contact professor to explain?
You should definitely contact the professor. English is just a trivial component in your application, so you should not worry about it. Especially, you will likely have an interview if you are shortlisted.

When I applied to Oxford, my IELTS score was only 6.5, while the school required 7 (and no band is less than 6). I contacted the professor, and she told her assistant (who collected the applications) that it was OK for that position with 6.5.

I was later rejected, but it was due to my lack of research experience, not my English score.