What follows is (a) a quick response and (b) just my opinion.
To start with, I don't believe that boxers were any more - or less - "exploited" during this era than at any other stage in the history of the game. And as far as "working class" boxers are concerned, the overwhelming majority of the boxers were what would be described as "working class".
Although you refer specifically to British boxers some of the examples below relate to American based fighters: (I'm just giving these to illustrate that some boxers did well in that Era, others in different eras fared very badly and might well have claimed to have been "exploited")
1: Jimmy McClarnin fought from 1923 to 1936 and had a wonderful manager who helped set him up for life - so you couldn't say Jimmy (as an example) was exploited in the Depression Era.
2: By contrast Joe Brown fought in the 1950-60s era, and there is a view that he was less than well served by his manager, being left very poorly off when the glory days gad gone. Likewise Billy Fox - of "Jake LaMotta took a dive" fame - was built up by his managers and then discarded when of no further use. So two non-depression era guys who one might think could have been treated a bit better. In a British context many people felt that Freddie Mills was "thrown to the wolves" several times by his manager - being matched against the likes of Bruce Woodcock despite conceding massive amounts of weight, and having tough fights with virtually no proper recovery time between them - but again, a non-depression era fighter (mainly 1940s)
I think the main issues were the fighter himself, the crowd he mixed with, and the lifestyle he chose to lead. I don't think your friend can really show that during the Era "working class fighters" were treated substantially better or worse than in any other era. There were - and will always be - good managers who care about their fighters, and by contrast managers/promoters etc who see the fighter as a warm body to be exploited for the next pound/dollar. The game is full of both types through evety decade.
Your friend might want to start his research by reading through Teddy Baldock's story - see
http://www.teddybaldock.co.uk/life/page_6.html
When you get to the last page of "Teddy's Story" on that link you'll see how Teddy basically blew his money on high living, and having no real notion of what to do once he had hung up the gloves. Exploited? Probably not - but maybe in modern times he might have been a bit better advised.
I'll stop pounding away at the keyboard as I may be pointing you and your friend in the wroing direction. But I'd just suggest that he may not find it easy to make a case that boxers suffered any worse in the Era than say miners, dockers, etc etc....or that they were worse off in that Era than in at other times
Hope this is some help. J