Well looks like I'm a bit late to the party here and terrible_one and Anthony have provided you with some really good information.
I will, unfortunately, add to the bad news. Sorry, mate but it's only fair to you.
First of all, here are some links to some organizations that you need to become familiar with:
CALEMSA: state government body regulating EMS for California.
Orange County EMS: regulatory agency for Orange County
San Diego County EMS: regulatory agency for San Diego County
National Registry of EMTs: national level certification and standardizing organization
Look over those sites and familiarize yourself with the information within them. Please feel free to direct questions to anyone here on the board.
So, back to the bad news. As previously stated California is the worst, most backwards state in the US for EMS. It is split up into about 55 county-level regulatory agencies that all operate with near-complete autonomy. That is, they set their own scope of practice, clinical practice guidelines (protocols), policies & procedures, and so on. There is a state-level standard for all of that, but each county is able to add or detract from it to meet their needs. You have to get "accredited" in each one separately in order to work there, which means you have to pay a fee each time.
It is unlikely that the state will recognize your UK qualifications (at least I am unaware of anyone from outside the US who has had success in recognition of prior learning) so you may have to go through one of the local paramedic programs. This by itself would be enough to discourage me from proceeding but it seems you don't have much of a choice. I would contact CALEMSA and see what they can do for you. Be advised, however, that they are grossly understaffed and subject to furloughs due to state budget issues.
Beyond that, you have two options for employment: Fire Departments and Private Ambulance companies (as you have discovered). It is possible to work as an ED tech in a hospital, but this is at the BLS level only. Paramedics are prohibited by state law from working in hospitals at the ALS level (thank the nursing associations for that).
Private Sector: Probably the largest employment sector, and where most new medics start out. AMR and Rural/Metro are the largest companies but the state is dotted with smaller operations. Most privates are IFT-only (yes, our wonderful healthcare system generates an absolutely enormous amount of transfers every day - most of which are completely medically unnecessary and are nothing more than insurance repatriations). Some privates have 911 contracts, but in Orange County this is at the BLS only level. In San Diego Rural/Metro and AMR both have EOAs (exclusive operating areas) for ALS 911 service in the southern part of the county. Regardless you will always be doing transfers as this is the primary source of revenue for these companies.
Pretty much all the privates are rather poorly managed, very unprofessional, very disorganized, and full of disgruntled, burnt-out staff. Wages typically start around $13-14/hour even for paramedics. You are under appreciated and looked down upon by supervisors, hospital staff, and fire dept. personnel whom you respond with. The ambulances themselves are often poorly maintained, with many hundreds of thousands of miles logged on the odometer, and equipment provided is often cheap and of suboptimal quality. Often management is stingy with resupplies and will restrict access to stock rooms. If you are lucky to have stations they are often unhygienic and lacking in basic amenities. Many private companies utilize a staffing system called System Status Management which means you don't respond from a station or fixed-location but are assigned to various "posts" supposedly strategically located throughout the response area. So, basically you get to sit in the ambulance all day bouncing around from post to post in between calls.
Fire Departments: The only employer of any desirability for paramedics, and the reason most people become paramedics in the first place. Pay is about 3-4x what you would see as a private medic. Excellent benefits. No IFTs except for the occasional instance where the hospital itself activates 911 because they have an unstable patient they can't manage and there is no time to call a private to transfer them. Top of the line equipment, ambulances, and immaculate multimillion dollar stations that are nicer than many people's homes. No System Status Management. Management is much more professional and organized and not out to justify its existence by finding infractions with which to exert disciplinary action.
Problem is, literally thousands of people will apply for maybe a handful of positions. Years pass between recruitment periods. If you do get passed the written exam (usually just a civil service exam) and get called in for an interview there are many things that can disqualify you. People have been disqualified before even getting to the interview room for not helping a secretary pick up papers she "accidentally" dropped (a common ruse). Should you be offered a position the probationary period is usually at least a year where you are treated like a slave often to the point of abuse, and can be terminated for any or no reason at all.
Then there is the "firehouse culture" aspect of things. This is difficult to describe. Maybe when you come out to visit schedule a ride along with one of the local departments and just observe the social dynamics of what's going on. Most of these guys do not care about medicine, and really only put up with it because it's what justifies their existence. Some departments are worse than others - indeed, getting assigned to an ambulance or squad is often used as punishment for some mistake you've made. Just something to be aware of.
Honestly, mate, this is not a desirable situation. As much as it sucks to hear this it might be best for you to look into nursing school. Nursing in the US is much different than the UK & Europe and is a much more developed and professional career path. You can even do a lot of work in EMS as an RN such as ground and flight CCT and 911 helicopter medevac. You can even challenge the paramedic qualifying exam as an RN and work as a medic if you wish. You might have more luck with universities here recognizing your qualifications so you can apply to an accelerated BSN program.
Hope this is helpful. Feel free to ask any more questions. PM me if you wish. Good luck.