I'm a non-native speaker of English from Poland. I'm 27. I teach English in the UK. My problem is that people recognise my foreign accent. Is it possible for me to learn perfect English pronounciation, so that others wouldn't realise I'm a non-native? Or at least make the accent less distinctive and speak as closely as possible to a native? If so, how to learn?

Chances are that you won't be able to completely get rid of your accent.
My husband is Austrian and he has been speaking English since he was a small boy (he is 37) and you can still hear his accent.
The only advice I can give is to practice! Ask people around you to point out any mispronunciations you make, therefore you can correct them and you will know what you need to work on.
Good luck!

You will naturally lose your accent over time and with practice. I am an Australian that has taught in the UK for many years- every time I spoke to my family in Australia they said I was 'losing my accent' and I am 30.

I have an Aussie friend who moved over with her Aussie kids. They got teased because of their accent so they taught themselves to lose it- they imitated the English accent when watching TV and generally kept practicing. It took them a year or two but it is very hard to hear their Aussie accent now.

Watch British TV and repeat what they say and how they say it. You will slowly lose your accent but it will take time and practice.

Gd Luck!

there are linguists, accent developers, and speech therapists who specialize in that for actors and such.

I believe that there are certain nuances in Polish and English, and when you identify them, you can practice minimizing their effect on your speech.

for example- in Hebrew and English, the R's are pronounced differently.

Be proud of your accent. I can't stand it when people move to a different country and drop their accent. You talk how you talk.