If you have an employee, there are lots of additional costs, and in particular you have a large National Insurance Contributions ("NIC") bill. If someone working for you is self-employed, you don't have to pay any NIC for them.
But the self-employed don't have the same rights as employees. They may have a better tax position though. They might be happy with this status, but not necessarily.
Some "employers" have been taking on workers and getting them to class themselves as self-employed. Sometimes this isn't accurate and the workers are giving up valuable rights if they accept.
Workers in gig economy ‘misled by employers over job protection’