However, as far as I can tell, anyone using any of the more established "big name" billing services to collect payments for a UK company is almost certainly breaking at least one law on a "your business is at risk" scale. Stripe would have to be very special to do better.
The usual culprits are VAT (I have yet to find a billing service that would actually allow a UK business to comply with its basic statutory requirements on this count, including several that claim to support VAT) and privacy (exporting personal data, such as names and credit card details, outside of Europe requires certain guarantees, which again I don't think would be met by any of the services I've looked into so far). I imagine quite a few businesses are getting away with using these services and not meeting their obligations, but personally I wouldn't want to operate with that sort of risk, particularly now Business Record Checks are becoming big news.
Stripe does seem to have a fairly clean API, but on the flip side, it also seems very limited in features next to some of the more established competition, so maybe it's just horses for courses. Again, I know that none of the other billing services we've considered this year even got close to supporting the basic charging model we wanted, never mind all the bells and whistles we've been considering, and if you wind up having to do a bunch of financial legwork yourself, these services start to look like very poor value for money pretty quickly.
IMHO, what small businesses in the UK really need is for the government to stop hassling banks about lending lots of money (sometimes useful, but not to many of us) and just get them to provide basic services like card payments in a sane manner: no multi-month waits to get up and running, directly comparable charging structures on some standard basis, transparent migration of customer card data between all the vault services without causing a PCI nightmare so there is genuine competition in the market, and so on.
And then I woke up. :-)