It isn't very clear what you are asking, Sandra. 'Is it common X as Y?' is completely meaningless. Are you asking whether the idiom "to be hand in glove (with each other)" has the same meaning "work very closely together"? If so, the answer is yes ... and no. This expression does mean working closely together, but nearly always in a negative sense, with an implication of dishonesty or corruption. For example, if a mafia gang is hand in glove with the police, this is not a good thing. I can see that you are keen to improve your English, especially as you are living in the UK, but please don't think that idioms are the key to language proficiency. To use yet another idiom, they are just 'the icing on the cake'. It is MUCH more important for you to concentrate on the basics of clear and accurate language first.

the expression is to "work hand in hand with each other".