Should you set up a limited company? It depends on the risk in the work, who you want to contract with, and whether the extra admin is worth it. It is not a tax trick, and it is not automatically cheaper than staying as a sole trader.
What a company actually changes
A limited company is a separate legal person. If the company is sued, your personal assets are normally protected, as long as you have not given a personal guarantee and you have not traded wrongfully. Clients, especially larger ones, sometimes insist on contracting with a company. You can also bring in another shareholder later, which a sole trade cannot do cleanly.
You will have accounts to file at Companies House, a corporation tax return, and usually a personal self assessment for salary and dividends. Those filings are public in part. A sole trader files one personal return and keeps more of the figures private.
The tax comparison, without the myth
A sole trader pays income tax and National Insurance on the profit. A company pays corporation tax on its profit, at 19% on profits up to £50,000 and 25% above £250,000, and you then pay income tax on the salary and dividends you take out. At a modest profit the two routes are often closer than people expect. At a higher profit, and if you do not need to draw everything, the company can be more efficient. We model both with your figures before you incorporate. We do not promise a saving.
When we usually say wait
If the profit is still small, the work carries little personal risk, and you want every pound in your own pocket, the company adds filings without much benefit. You can incorporate later. The other way, closing a company, is slower.
If you want it checked properly, start with company formation and the limited company accountant page, or book a free accounting review.