If you create a limited liability company it becomes a separate entity (a legal person) from you. The law treats its property and business as different from yours. Of course that is what you want because it means that, as a general rule, if the company becomes insolvent, that will not rebound on you. Its debts are not your debts.
What this means is that you don't "convert" your existing business into a limited company, rather you create a company and then transfer your business (or part of your business) to it. If tax is important to you, you might want to research how to do this so as to obtain the best tax outcomes. I'm a lawyer, so I am not the best person to ask - an accountant should know.
Setting up a limited company is easy. There are lots of websites that will do it for you electronically for tens of pounds. I'd suggest browsing what's available using a search engine. They all seem much the same. You can do it yourself, but if your time has any value, reading the Companies House guidance (which is good) will probably be less cost-effective.
I think you need to work out why you would want to do this. Its perfectly sensible if you want to reduce your risk from a website which is becoming commercially significant. A limited company doesn't insulate you from all risk. You might find either taking some specific advice or asking more focussed questions (here or on other forums) would help.