The Treasury are currently looking at ways to increase competition in the UK's payment space. Their ideal outcome is a world where many payment networks can co-exist and compete. Here's how it could work:

The above provides a viable model for innovation at the payment network level:
GoCardless operates similarly to the above, with Direct Debit as the link with the banking system:

The above works well for GoCardless, where we deal with payments that don't need to be instant (typically invoice payments).
Unfortunately, Direct Debit isn't a good enough link with the UK's payment infrastructure to allow new instant payment networks, which could be used in e-commerce. For the innovator's new network to be instant, their underlying link must also be instant, and Direct Debit payments aren't (they take at least 2 days). What's needed to create competition in the e-commerce payments market, and beyond, is a new, instant bare-bones network backed by the UK's faster payments infrastructure.
Fix the underlying link with the UK's payment infrastructure, and anyone would be able to safely innovate on top of it. You'd have a safe but competitive market at the payment network level.