Is the "I accept" Button usually enough?

In many jurisdictions, to obtain consent for any e-contract and/or Privacy Policy it is necessary that the documents are shown to the user (or at least accessible via hyperlinks) prior to clicking on the "I accept" button. As Lawrence said, there are some provisions that could be problematic, for example if the e-mail address is obtained for commercial or advertising purposes (SPAM).
Regarding Data Protection, in some cases is necessary to obtain a prior written consent when sensible data is collected.
Nonetheless you are established in the UK, if your website is available for people located in other countries you should comply with the laws of such country.

Click-thru licences have been accepted so long as terms policies visible and no surprises. However privity of contract is modified by legislation, eg australia has laws against onerous terms of big companies being imposed against smaller and of course, certain consumer protection laws cannot be exempted. EU Data Protection Directive governs all privacy issues of their citizens including email address. Getting into trouble is a function of how outraged a user would be and their willingness to take it to authorities so perhaps a better question is whether you,re trying to do anything outside existing norms.