Travel advice on UK to Colombia via Miami please!?

I am looking for the cheapest option to get from the UK - London or Midlands airports to Miami, USA where I will stay for a few days before flying from Miami to Bogota, Colombia. I will remain here for 10 days and then fly back to the UK. Can anyone give me any airlines that would do these flights cheap, i am happy to go via any country as long as its cheap!!!