When registering on Amazon UK, the sole proprietorship form is as follows:

1. First, on the registration page of Amazon UK, select "Legal Proprietorship" as the business type.

2. In the "Company Name" column, fill in your company name.

3. In the "Legal Person Name" column, fill in your name.

4. In the "Legal Person Address" column, fill in your detailed address, including street, city, province/state, postal code and country.

5. In the "Company Registration Number" column, fill in your company registration number.

6. In the "Value Added Tax (VAT) Tax Number" column, fill in your VAT tax number. Please note that according to UK tax law, sole proprietorships also need to apply for a VAT tax number.

7. In the "Bank Account Information" column, fill in your bank account details, including bank name, branch name, account number, Swift code, and billing address.

8. In addition, you also need to provide your contact information, such as email address and phone number.

9. Finally, read and agree to Amazon's Seller Service Agreement, and then submit your application.

During the filling process, please make sure all the information is accurate to avoid problems during the registration process. If you encounter any questions during the filling process, you can refer to Amazon's Help Center or consult a professional consultant.