I agree that the very first interview in a foreign language might be nerve-wrecking for anyone. I wouldn't suggest saying "my English needs to be improved" or anything like that. If your interview is in English, it's already assumed you speak English. Though it's easier said than done, be confident in yourself. Or at least fake it til you make it :)
I would definitely spend time doing several practice interviews with native English speakers so you get more comfortable with it. Before your interview, PRACTICE. After your interview, PRACTICE!
Good luck with everything.
I think it has something to show in your comment that you started to make mistakes when you talked about the interview. It really would be a good idea for you to take a look at some relaxation techniques that you can carry out before the actual interview,, It worked for me!
You obviously have a very good level of English, so honestly, I think the only thing you really need to concentrate on is practacing a little conversation, but asking people to be a little more formal, when they speak to you, it really doesn't matter who, I think you'll find that you only need to believe that you are capable of going through a formal interview. It also really helps to ask those around you who you speak with if there is any type of improvement that you can make to the various abilities that are necessary to speak in general, such as pronunciation, entonation etc.
Other basic tips, try not to construct very complex ideas, this, in my experience can lead to a loss of sintaxis, making it very difficult for the interviewer to understand. Answers can be surprisingly short and complete in English. And last, but not least, be proud of your English level, I am sure you will do really well.
Hope I helped a little!
The first time will probably be difficult regardless of your language skills, but you shouldn't worry too much because the interviewer will understand your situation. The first time I was having a job interview my English somehow mysteriously degraded, but they were happy with me nevertheless. It gets easier later, though.
Prepare as much as you can. Practice, alone or with someone. Look up the words you may need. Think about what they may ask you and what you will say. You can even ask someone to simulate a job interview with you. But do it in advance and don't think too much just before the interview. Before and during the interview the most important is to relax, I know it's easier said then done, but try to apply whatever you already know that helps you or whatever relaxation techniques you can find.