I’m planning to register a private limited company in the UK but I’m unsure about the financial side. What’s the minimum capital required to start a private limited company? Do I need to deposit a certain amount upfront, or can it be symbolic?

In the UK, it’s very fast (48hre) and cheap to start a private limited company.
It costs only £12 to register a company in the UK. The steps to set up a private limited company are quite simple. You need:
A company name
An address for the company (UK)
At least one director
At least one shareholder
The agreement of all the initial shareholders – memorandum of association
Details of the company’s share and the rights attached to them – statement of capital
Written rules about how the company works – articles of association
Then you can register online with the Companies House if you standard articles of association. Otherwise, you will have to register by post, using an agent or a third party software.
You will also need to register for Corporation Tax within 3 months.
To form you UK company seamlessly: https://businessglobalizer.com/services/uk-company-formation/