Is there a standard set of terms that could be used to include (for UK website), that would cover me, asking a user for First name, surname, username, email address and an opt in for communications from me?
since you say you're running a UK website, the best reading you can do is on the ICO (which is among the better agencies worldwide when it comes to guidance imho).
You'll find pretty much all the answers you need. If you don't want to spend too much time educating yourself, you might be interested in the work I'm doing at iubenda, where we create software tools for online compliance. There are completely free tiers as well.
In general you'll want to cover at least the following sections as outlined by the ICO currently:
- your identity and, if you are not based in the UK, the identity of your nominated UK representative;
- the purpose or purposes for which you intend to process the information; and
- any extra information you need to give individuals in the circumstances to enable you to process the information fairly.