There are significant tax savings, and theoretically limited liability. The significant tax savings will change next tax year with changes in dividend taxes and NIC contributions. No-one is really sure of the actual impact at this point.
The rates for dividend payments are set but because of the triple changes of the budget - dividends, employment allowance and travel/subsistence expenses, it could affect some contractors a lot worse than others. Though it's mostly those who rack up large commuting/accommodation expenses chasing high paid work in London while not living anywhere near there. The travel/subsistence rules haven't been set yet but it's likely HMRC will crack down on them quite hard.
In addition to the benefits you get as the contractor, agencies also don't want to hire sole traders as it could be argued they are actually employees. This would mean it's the agency's responsibility to withhold taxes, and the contractor would have rights to things like holiday and sick pay.
I would say the biggest advantage of a Ltd company is that company owners aren't required to pay their company’s debts beyond the value of their shares. Also, it offers a very tax-efficient methods to take money of the company. This is why you probably need to go to a company formation agent. They will be able to advise you on this matter. Try sending an email to these guys - https://www.formationsfactory.co.uk
This depends on a country (sure, I understand the original post is about UK)
Say, in Russia one'd generally would want to go sole trader route and not an Ltd one. Less initial paperwork, a bit more relaxed tax/accounting rules (with same rates), and significantly simpler to put earned money into your wallet.
You can go the "Self Employed" route in the UK just easily, it's a simple online registration and you get a VAT number and a tax code, but you really don't want to do that.
If you are self employed there is no liability protection that separates you from the business this means that for the business to go bankrupt you have to also go bankrupt, and worse creditors can go after your own and familial assets to clear debt that was incurred by your business.
Now in some rare cases when there was gross and often criminal misconduct the liability protection can be lifted on a business which means it's stakeholders can be found liable for damage but that's quite rare.