There isn't the same cultural background in BE. It is possible that the same term might be used, or a different job title. You should probably consider that there isn't a generic term in BE the way that there is in AE.
The American job is described at Camp America's website -> Counsellor.
As Glasguensis points out, this is not a British concept (and, as far as I am aware, it is not a concept in the rest of the BE-speaking world.)
The job might be described as 'group/team leader', unless it were, for example, the Boy Scouts/Girl Guides, in which case they probably have specialised terms. But, as usual, a full sentence with some context would help.