£5. Enter some forms and that's it. They offer a registered office package; they'll be in the UK for you. I registered a company through them (although I used a more expensive package, including stuff like registered office) and saw no indications I had to be UK based (although I am)
This is the real deal: http://www.companieshouse.gov.uk/
I'm from Poland, and every single bank in UK asks me not only about my company office's address, but also the founder/director address. Living outside of UK (although still in EU), I found no way around this yet.
Which part of UK are you located in?
I get free postage paid envelopes so I can mail stuff to them as well. It's good.
If you want to get incorporated in Delaware and you don't have a statutory agent there it is going to cost more money to get someone to forward the mail for you, also you need to be aware of any rules or regulations for that state for opening the business.