And who says all British magazines speak English correctly?
My way of thinking about this one would be that we use the nominative case ('I', 'he', etc.) when the subordinate clause refers to its subject (sorry, I don't know how to say this in grammatically correct terms), as in 'It is I who have to apologize', and we use the causative case ('me', 'him', etc.) when the subordinate clause refers to its object, as in 'It is her you should take with you.'
Collins English Dictionary says:
Although the nominative case is traditionally required after the verb 'to be', even careful speakers say 'it is me' (or him, her, etc.) rather than 'it is I' in informal contexts.