It is true that during WWII the BBC had broadcast coded messages to British secret agents behind enemy lines, and that some journalists had worked with MI6 in producing propaganda.

BBC: The 'secret agents' of the UK press

Given its assertion that states base their foreign policies on unsentimental assessments of their national interests, true realists would argue that there is no rational bar to enemy states sharing the same allies if doing so advances their national interests.

CENTERFORSECURITYPOLICY: Israel and the 'realists'