Hi Piqla,
NATS, like all Air Traffic Services, require a certain level of English as I believe is stipulated by the ICAO. I can't tell you if you can meet that or not, but you certainly seem reasonably proficient (OK your post has a few typos and some grammatical mistakes... but generally I find it easier to speak another language than write in it). I'd recommend doing some homework regarding what is required.
In your own country you failed at selection. I'm not sure I'd describe this as having 'failed at being an atco' and I don't think NATS would have a problem with this. NATS themselves will let applicants who have failed at selection apply again once a year up to three times, and it is not unheard of for someone to pass on the second or third attempt. I don't see how they would treat someone who has failed selection in another country as any different. This shouldn't be an issue, but I would advise that at interview (if you get that far) that you are clear with them that you failed at selection, not training or validation (I would imagine that someone who has failed at these later stages may need to be dealt with differently).
Out of interest, do your own country's ATS not allow you to reapply if you fail selection as we are allowed to here? This would seem like a far easier option than uprooting yourself to the UK if possible.
With regards to your country of origin. Yes it is true some British people are not very friendly towards Eastern Europeans... this is called racism, and whilst it is permissible in the UK for an individual to hold racist views or opinions it is illegal for a company to descriminate on these grounds. If you have a legal right to work in the UK then NATS will consider your application in exactly the same way they do everybody else's, your ethnicity will not be a factor.
Finally, just to point out in case you hadn't realised, NATS use the Strip Display test in their selection too, so you will have to pass it to work here as well.