Can I claim for client lunches and entertaining?

Unfortunately no, client entertaining (meals, drinks, events, gifts to clients) is specifically disallowed for tax purposes even though it's a genuine business cost, so you can't deduct it from your profits. This is one of the most common misunderstandings among self-employed people, so it's worth budgeting for it separately rather than assuming it will reduce your tax bill. Staff entertaining, such as a modest annual team event, is treated differently and may be allowable within certain limits, so ask an accountant if that applies to you.