I received a lot of emails from parishes in Luton last days with no informations about Stefan. But one parish told me that I shoud also ask St Mary parish in Dunstable and also cemetery in Dunstable and it seems that they were right. Cemetery in Dunstable gave me informations that they have a record. It was not Stefan Swider, but Stefan Sinder, who was buried in 1956 (9th February). Initially I thought this is different person, because of different surname and month but:
-based on FreeBMD database, there is no Sinder who died in UK in 1956
-I have seen photo with grave and I thought it was March headstone (number looked like '3'), but quality of the photo and espiecially distance from headstone can suggest that it could be '2').
Especially that there is no Sinder who died in UK in 1956, I'm rather sure that this is the same person who I'm looking for

They also informed me where he was buried ( " in plot no: RC 41." - I don't have cemetery map with sections but this is important information) and gave me his last address (and this is Luton so correct).
I did a terrible job to trying to locate this grave on Dunstable Cemetery on West Road on bing maps (google maps were too poor). I know that it sounds unreal but I think I located this grave on bing maps. Of course it's from distance and quality isn't very good but I believe it's not my imagination. As grave was very original, headstone was like a cube with St Mary ahead of this
headstone so it was not impossible as there were not many graves like this. I also know that behind this grave, few rows later were headstones with a lot of crossess and on bing map I located this place too and place of Stefan's grave is exactly in perfect place in relation to this graves with crossess. There were also houses with chimneys in the middle of the house behind the cemetery and the same houses with chmineys I see on bing maps (place called Meadway). I checked date on bing maps and if date is correct this map was created October 2011, so this grave was still there in 2011.
The amount of information I got is amazing, it's beyond my imagination. I know his last address now (we checked this house later on Google Street View - it's great). I know where was the funeral (St Mary Dunstable), where his grave is (Dunstable Cemetery, plot RC41), I was able to locate this cemetery on bing maps and I found grave with looks exactly like this, and the other graves seen on my old photo from 60s looks the same. I never expected that I will get so many informations.
So thank you very, very much to all people in this thread, to all parishes and cemeteries in Luton, and especially to St Mary Dunstable parish and Dunstable Cemetery.
I did this for my father, who is 73. I don't know so many words in English to explain how happy he was when I told him about this.