The idea of using Barclays, or any 3rd party bank, is just to get enough traction so they have their own participation method later. Also it doesn't show Barclays on the statement from my usage - it shows the end merchants details. I didn't really know it was Barclays till now.

Barclays has been known to help startups by lending them their (global) infrastructure in the UK. Another Example is Dopay where Egyptian Barclays ATMs have been lent out.

The Bank of England is moving towards allowing non banks to participate in the payments system by 2020, its supposedly blockchain secured so it goes a notch above what a sole bank/firm could do. Revolut could theoretically switch from Barclays then.