Since I have been over here for a while, its now started to become common for friends of mine to ask me to give advice to others on teaching in the UK. Here are a few main points:
I don't know how much you already know but, I was an Australian trained teacher who moved over to London about 2 years ago. I started teaching in the UK school system through agency work, before getting a short term contract at an international school which turned into an ongoing position and loving it.
There are a range of employment options. You can apply directly to the school or work through a agency. Agency work can be short term supply (daily supply or substitute teacher), long term supply (term, semester etc placements) or permanent work. Short term supply and long term supply may give you a higher rate but you may not get paid for days you don't work or holidays (pro rata) - so make sure you ask your questions to the agency or school to clarify. You can choose what best suits you or mix it up. When looking at schools its good to do your research. There are MANY school in the UK and many different types of schools, areas, specialist schools, demographics and standards. Schools get inspected by OFSTED where you can see their rating and report. There are comprehensive (public school), grammar (select entry), catholic and independent schools.
The UK has introduced a National Curriculum for math, science and english. The UK system uses "Key Stages" describe levels - if your high school, you will be looking at Key Stage 3 and higher. They have GCSE's and A levels for university entry. It all sounds confusing at the start but it makes sense eventually. When you get to interview round its good to have a little background and familiar with the terminology. If overseas, interviews can be conducted via Skype or phone.
International Schools in the UK:
As for international schools, they recuits mainly from recruitment expos, which I have heard are an experience in themselves - but they also use agencies to fill placements, like in my initial situation. I was a "local hire" as i was already in London and was found through one of their London based agencies. International school may follow the IB program or their own curriculum (i.e. US education system etc).
As far as teaching agencies go - it can be a real mix! Don't be frightened to sign up to a few - after all the wider the search, the better chance to find a school that fits you! Some can promise the world and deliver very little - best to go from others personal recommendations! ;)