I believe that your options are:
1) You could enter on the tourist visa waiver program (just go over and visit) for up to 6 months. You have to be able prove that you have funds to support yourself and that you have every intention of leaving before 6 months if you are questioned at immigration.
2) If you are currently enrolled in or recently out of college/university you could get a BUNAC visa, which would allow you to live and work in the UK for 6 months.
http://www.bunac.org/usa/workinbritain/ How the Program Works
The Student Exchange Employment Program Blue Card provided to Work in Britain participants acts as an entry visa and allows US university students and recent graduates to work in Britain for up to six months. The program is approved by the British Government and is a reciprocal work/travel exchange program. The Blue Card is available to eligible US citizens or permanent US residents, aged 18 and upwards.
3) Depending on your qualifications you may qualify for the Highly Skilled Migrant Program (HSMP) visa.
http://www.workingintheuk.gov.uk/working_in_the_uk/en/homepage/schemes_and_programmes/hsmp.htmlWhat is the Highly Skilled Migrant Programme?
The programme is designed to allow highly skilled people to migrate to the United Kingdom to look for work or self-employment opportunities. The scheme has a separate assessment for applicants aged under 28 as well as an assessment for those 28 and over.
The Highly Skilled Migrant Programme is different from the work permit scheme because you do not need a specific job offer in the UK to apply.
It is different from business routes such as the Innovators scheme or other business categories because you do not need a detailed business plan; you do not need to create jobs; and you do not need to invest in the UK.
4) If you work for an international company with offices in the UK you may be able to get a transfer to the UK.
5) If you are uniquely skilled you might be able to get a work permit (but I believe that company has to prove that they advertised the position, held interviews, and were unable to fill the position with any candidates from the UK or the EEA - European Economic Area).
If you tell us a bit more about your situation, I'm sure others on the site will have recommendations for you.