Is it possible to lose your English accent when speaking Polish? Has anyone managed to?
I'm not sure why you'd want to lose your English accent - it's very possible to pronounce Polish well with a British accent just as it's possible to pronounce English well with a Polish accent. Great Garbo pronounced English very well with a Swedish accent and there are many more similar examples.
The key, however, to good pronunciation is practice (a lot of practice) and not being afraid to sound a bit outrageous, even though it might not seem natural. Once you get used to forming the vowel sounds (and the soft consonants) you will be fine.