> [Paymill] also require some business information and identification from you, but this does not appear to be particularly stringent
Actually, speaking from personal experience, it is particularly stringent. I had to give up in the end because the bureaucracy was taking too long.
From memory, you need a tax identification number, your VAT identification number a scan of your passport, to display your name and home address on your website and you need to post it all to Munich. I suppose this doesn't sound like too much but in the UK you have no reason to have a tax identification number unless you're self-employed and already trading. In the UK you don't have a VAT id unless you're making £77k. Outside Germany showing your home address on the web is considered a bit crazy. Consider now that if you're trying to get Paymill to authorise you are probably are not trading yet. It's not that appealing and I would recommend against it unless you have time to spend exchanging emails with customer service representatives who have a poor command of English.
Paypal's (admittedly lame and APIless) method of payment acceptance is to copy and paste a button.