Unfortunately, I think Braintree in the UK is probably doomed at this point.
They looked good a year or two ago, and we did consider using them. They were certainly a better prospect than old school card payments where you had to apply for multiple services, make back room deals to get good fees, and all that nonsense. However, to start the application process with Braintree, it seemed you would still be faced with a lot of form-filling, followed by multi-week delays to get approval (or not), and on top of that the fees were unclear but didn't look competitive in most cases.
More recently, the likes of GoCardless and Stripe have become serious players on the UK scene, and both seem to be working on expansions further into Europe as well. They have all the same obvious benefits that Braintree offered: a single company to deal with, staffed by human beings rather than robots, reasonable APIs. But they also offer much faster sign-up and reasonable, transparent fees.
At this point, to be brutally honest, the likes of Braintree are simply outclassed. Unless anything very surprising happens, I expect the payments market for UK and probably European small businesses and start-ups to be completely dominated by GoCardless and Stripe within 2-3 years. Unless you're big enough to approach the old school players with enough leverage to get favourable terms, it's hard to see why you'd look any further if these are options, and I think both GoCardless and Stripe will do well because they're different enough not to be in direct competition but similar enough to keep each other honest.