The CIC Regulator writes:

The Regulator of Community Interest Companies would be satisfied with a relationship between a community interest company (CIC) and an ordinary limited company as long as consideration is made to the following points:

The key thing is to ensure the CIC’s dealings with the limited company are open, transparent and accountable and the bank accounts and books are completely independent of each other. 

More information on the Office of the Regulator of Community Interest Companies can be found here