I registered my interest a while ago but they haven't given me one yet, so I wouldn't say they offer business accounts, so much as they're going to/are testing this.
Starling does offer business accounts now, but you can only have one Person of Significant Control, i.e. over 25% owner. There is no monthly fee with their offering though, so it's probably the better offer.
Note that Starling will prevent you opening a business account if you've held a personal account in the past and closed it. That was the position I found myself in.
For what it's worth, I've seen some suggestions regarding business account pricing on the Monzo Slack, and there are plans for separate tiers (including a free tier which lacks some of the more advanced accounting integrations).