If you are a non-EEA (European Economic Area) or Swiss national, you will need a work permit or visa to work in the UK. The most common way to obtain a work permit is to have a job offer from a UK employer. However, it is still possible to obtain a work permit without a job offer in certain circumstances. Here are some options:

1. Highly skilled individuals: If you are a highly skilled worker, you can apply for a Tier 1 (Exceptional Talent) visa, which allows you to work in the UK without a job offer. This route is designed for individuals who are recognized as leaders in their field, have won international awards or have been endorsed by a recognized UK body as an exceptional talent or promise.
2. Graduate route: If you have completed a degree in the UK, you may be eligible for the Graduate route, which allows you to stay and work in the UK for up to 2 years without a job offer. To be eligible, you must have completed a degree at undergraduate level or above at a UK university, and have a valid Tier 4 (General) student visa or a Student visa.
3. Start-up visa: If you are an entrepreneur with an innovative business idea, you can apply for a Start-up visa. This visa allows you to set up a business in the UK without a job offer. You must have an endorsement from an approved UK endorsing body and meet other eligibility criteria.
4. Innovator visa: If you have an innovative business idea and have at least £50,000 in investment funds, you may be eligible for an Innovator visa. This visa allows you to set up and run a business in the UK without a job offer. You must have an endorsement from an approved UK endorsing body and meet other eligibility criteria.
5. Global Talent visa: If you are a leader or potential leader in science, engineering, medicine, humanities, digital technology, arts and culture, or research and innovation, you may be eligible for a Global Talent visa. This visa allows you to work in the UK without a job offer. You must have an endorsement from a recognized UK body as a leader or potential leader in your field.

Please note that the above options have their own eligibility criteria, and the application process can be complex. You should consult the UK government’s official website for detailed information on each option and the requirements.

Here is some more information about each of the options I mentioned:

1. Tier 1 (Exceptional Talent) visa: To apply for this visa, you must first be endorsed by a recognized UK body in your field. The endorsing body will assess your achievements and potential, and decide whether you are an exceptional talent or promise. Once you have been endorsed, you can apply for the visa. You will need to show that you have enough money to support yourself in the UK, and meet other eligibility requirements.
2. Graduate route: This route is available to students who have completed a degree at undergraduate level or above at a UK university. To apply, you must have a valid Tier 4 (General) student visa or a Student visa, and apply within 2 years of graduating. You will need to meet other eligibility requirements, including having enough money to support yourself in the UK.
3. Start-up visa: This visa is designed for entrepreneurs who have an innovative business idea and want to set up a business in the UK. To apply, you must have an endorsement from an approved UK endorsing body, and meet other eligibility requirements, such as having enough money to support yourself and your business in the UK. The endorsing body will assess your business idea and your potential to succeed.
4. Innovator visa: This visa is for experienced entrepreneurs who have at least £50,000 in investment funds and want to set up a business in the UK. To apply, you must have an endorsement from an approved UK endorsing body, and meet other eligibility requirements, such as having enough money to support yourself and your business in the UK. The endorsing body will assess your business idea and your potential to succeed.
5. Global Talent visa: This visa is for individuals who are recognized as leaders or potential leaders in their field. To apply, you must have an endorsement from a recognized UK body, and meet other eligibility requirements, such as having enough money to support yourself in the UK. The endorsing body will assess your achievements and potential, and decide whether you are a leader or potential leader in your field.

It’s important to note that the application process for each of these visas can be complex, and it’s a good idea to consult the UK government’s official website for detailed information on the requirements and application process. Additionally, if you have any questions or need help with the application process, you may want to consult an immigration lawyer or a qualified immigration advisor.