Works fine with BA -
I've used before with flights on different airlines and hotels all under one itinerary, and it comes with one trip itinerary and bill. They seem pretty proactive too on the rebooking side during IRROPS.
Since they're also in the SaaS / tech space, I'm very aware of their quick growth. They're actually the fastest growing startup in Europe right now:
https://saas1000.com/
Not hard when the competition is Concur. I spent an LHR-ORD flight half watching IFE, and half watching someone try to search and "buy" a transaction on Concur (747 with the wifi enabled).
I'd use TravelPerk for everything it weren't for the lack of trains (coming soon), BA Holidays inventory (which I use to for US trips in the same week), and the ability to earn extra Avios booking direct with holidays.