There are ways to gently inform the person(s) of your discomfort. If communicated well, it can be settled. In one case I dealt with, body odour of someone on my team was causing another person distress, but some gentle, kind advice (yes, it was embarrassing as hell so we did it in private) and a quick trip by him to the shops for some deodorant resolved the problem almost instantly. Here's hoping.
Why should the onus be on me when they are the disgusting ones and the employers are at fault for not offering showers?