Hi,
Sadly, this is the reason that so many universities are now looking for further maths. Very few schools now have the resources and expertise to teach engineering type courses, so students enter with far less knowlege and experience in this field. The universities therefore have more teaching to do and as a result, need students who are proven to be better at the maths content of the course. I really wouldn't worry about it too much. It's a great opportunity for those with access to it, but the unis do understand how few people do get these opportunities. They certainly won't have expected you to change school!
I was worried you would ask about the interviews, as there is a huge variation in what they ask, purely depending on who interviews you. I don't know how specific I am allowed to be, but I can probably say that my interviewer was more involved in EIE than EEE. We started off talking about my personal statement and went through the usual why engineering, why Imperial type questions, before talking about some general topics in electronic engineering, like how can electronic engineers improve x product. Then we talked a bit about sub-systems within an electronic product (smartphone) and how each could be developed. Finally, we talked a bit about algorithms (don't worry, this was really basic) and then optimization (you may well cover this in your programming), bringing this back to the smartphone.
I know that I was very lucky. These are all topics I was interested in and already knew at least something about. Talking to other people in my group, some were asked straight maths questions (calculus, trig, expansions etc.) for the whole interview and some got weird logic puzzles. It's fair to say that you really can't prepare for these interviews beyond the 'standard' interview questions. I really doubt they'll ask you specific programming questions.
Also, don't get too worried about which course you apply for. You can move between year abroad, management and the 'normal' course (as well as the BEng and MEng) at any point until the end of the second year. You can even change between EEE and EIE during the first couple of weeks! Getting on the year abroad is absolutely down to your choice, although if there are too many students wanting to take it (I don't know if there is a limit) then priority would be given to those who applied to it originally. I didn't know about EIE giving lower offers. It is a smaller course, so might not be as popular.
As long as your work experience is in an engineering field, it is not useless. Rolls-Royce is hardly an electronics company. The point is that you've seen how an engineering company operates, and have some industrial contacts. The other placements sound great.
I don't have a CV as such, but I don't mind showing you my personal statement. Unfortunately, my head of sixth form was very clear that we weren't to show our personal statements or applications to anyone until our places are confirmed. I'll post back when I can.
Good luck on results day!