I know many examples of consultants who have worked in Scandinavia without speaking the local language. So English should be sufficient in a significant share of the projects.
However, most of these people that I know have transferred to a nordic office within the firm - you will need to find out what the formal recruiting requirements in terms of language are for each firm. But this should be quite easy - just reach out to HR/recruiting and discuss the matter! This is what these colleagues are there for.