By far the most important advantage of a limited liability company is just what the name indicates: the company's liability is limited. In short, that means that if the company goes bust, the creditors can't expect repayment from the owners' (shareholders') personal assets.
In some cases - such as substantial loans, mortgages, etc. - the lender might insist on a personal guarantee from the owners, but that doesn't normally apply to day-to-day transactions.
Neil mentioned the saving on Class 4 NICs. Unfortunately, that's offset by the additional cost of Employer's NIC, at least on the salary element of your income. On the other hand, in the case of a small, private company, where the directors are also the owners, you can pay at least part of the directors' remuneration as a dividend rather than salary. You escape NIC completely on dividends, and the personal tax treatment is more favourable. The previous government were trying to change that, but I don't know if the present government have the same attitude.
Apart from the question of limited liability, the benefits of a limited company will depend a lot on the nature of the company and on the owner's circumstances, so it's worth getting professional advice if you are seriously considering the move.
Mike