Incorporation in the UK does not require citizenship. The best option is certainly to find a reliable company formation agent who can complete the registration for you. Their services generally include free customer support, business banking advice, company type recommendations, free pre-submission reviews, address services, free accountancy consultation, domain names, etc. Be very careful and read the reviews about the formation agent you choose. Confirmation of incorporation is usually received a couple of days after submitting all the documents to the agent.
The next steps you'll need to take to actually begin functioning in the real world are usually:
- Decide whether you want to register for VAT (and charge VAT on all your sales and deduct VAT on your purchases). This is compulsory if the company revenue goes beyond £80k in a 12 month period.
- Start a business bank account. This is a difficult step, UK banks are extremely reluctant to prevent money laundering and formation agents only can offer an introduction to a bank. Paypal can be used as a temporary alternative.
- Registration with PAYE if you have any employees.
Last but not least, you may also need to apply for visa if you are not European and you are planning to stay in the UK while running your business. The exact rules and conditions for a visa are pretty complicated depending on your circumstances, so please check the government website.