4. Note functionality, examples and the practical stuff
List any specific functionality: online booking, ecommerce, a particular payment provider, a CRM or mailing-list integration, multi-language, a blog you will update yourself. Each of these has cost and platform implications, and surfacing them up front avoids the expensive surprise of discovering a requirement halfway through. Also share two or three websites you like — competitors or otherwise — and say what you like about each; showing is far clearer than describing.
Finally, the practical realities: your rough budget range, your deadline if you have one, and who the decision-maker is. Sharing a budget is not naive — it lets a good designer propose the right scope for your money rather than guessing and quoting something you will reject. A brief that includes the goal, the audience, the content situation, the functionality, reference sites, budget and timeline lets a London designer give you an accurate fixed price and build you a site that actually does its job — which is the whole point.