Zhenya - the anglo is easy to play in about two keys. Singing with it is certainly possible, but unless you can get an anglo in keys compatible with your songs it won't be much use. A chromatic anglo can be played in more keys, but it gets harder which may be a distraction from singing at the same time.
There is a tradition of using anglos for Irish music that goes back to a time when anglos were cheap - there's no reason not to play Irish tunes on an English concertina and it's really a more sensible instrument for that. If you've found it a good instrument to sing with then maybe you should stay with it.