I want to travel to the USA (I am UK Citizen) and I am only allowed 90 days.
Is it possible for me to stay longer - say 6 months to a year, and how?
The only way to stay in the US for more than 90 days is to obtain a B1/B2 visa, which will allow you to stay up to 6 months.
However in general the US is relatively strict regarding granting B1/B2 visas to people who are otherwise eligible to use the Visa Waiver Program (which allows for stays up to 90 days). Generally they will be looking for a very good reason that you intend to stay for more than 90 days, and some level of guarantee that you will leave at the end of your stay.
Unfortunately visiting a girlfriend generally doesn't tick these boxes. A 6 month stay also means that it's likely that you don't have a job to return to in the UK, and probably don't have a permanent UK residence to return to - if these are both true then your odds of having a visa approved are reduced even further.
The problem then becomes that if you do apply for a visa and it is rejected, you are no longer able to enter the US using the Visa Waiver Program - which means that you can't visit your girlfriend at all.
Nobody here can give you a definitive answer as nobody knows your exact situation or how the consulate staff will interpret that situation - but if it were me I would NOT be risking applying for a visa.