If one of the universities you have contacted let you know that they would formally consider your application then you will now need to start work on a UCAS application.
As you are looking to transfer university then I will assume you have already been through this process and it is pretty much the same. One of the main differences is that when entering your course choice you need to state that it is for entry point 2 (if that is the year you will be entering at). Obviously change this dependent on your circumstances – could be 3.
You will need to pay for all of the normal processing fees associated with this and the same rules apply with regards to choices and the amount charged.
As before you will receive the decisions through track and would have to accept or decline in the same way.