The photo is blurry and the provided backstory is thin on details, so this partial answer is conjectural. One thing is clear to me, though: this is a picture of a happy man.
The subject is wearing what looks like a uniform of the Polish Army in Exile, which played an important role in World War II. (There is a section on these uniforms in a book Military Uniforms in Europe, 1900-2000, by R. Spenser Kidd, pp.82-83.) This army was equipped by the British, and the basic fabric and cut of the uniform was the same as the British Army's. The shape of the breast pockets and the beret are two obvious features illustrating this.
The cap badge, however, looks to me like the standard Polish Army cap badge, illustrated here and here. The smooth curved bottom outline of the badge is visible in your image, and the lumpy upper outline in your image seems consistent with the spiky outline of the badge.
The rank shown on the shoulder straps seems to be that of a "Starszy szeregowy", private first class.
The meaning of the badge on the breast pocket is unclear to me. It looks a bit like a medical unit badge, but I think unit badges were usually worn on the shoulder.
I suggest you contact the Pilsudski Institute in London to see if they can tell you more about your relative and his photograph. They might be able to look his name up in various unit rolls.