Unless you have any complex or unusual requirements for the corporate documentation (memorandum and articles of association, the 'mem and arts'), you can do this yourself by applying to Companies House by post or online.
Ensure you have selected an appropriate name for your company before you begin: one that is not the same as or similar to a trading or registered company name that is already taken, or to a registered trade mark held by someone else, and which is not offensive.
Check company names and trade marks databases first. You can do this, and get a lot of clear guidance, on the UK government website:
However, you will need to remember to carry out all company secretarial duties going forward, filing regular reports on behalf of your company, and you will need to arrange the registered office address for your company.
If you would like to instruct a law firm to form your company and perhaps prepare bespoke 'mem and arts' for you, fill out the form and below.