I doubt this is from Eastern Europe: that's very clearly British Battledress, and I lean towards Royal Artillery for the corps owing to the shape of the cap badge and the white lanyards. The badges above their stripes could also be that of a Master Gunner. The man third from the right in the back row also wears his badge on the lower sleeve, which is a distinction peculiar to British Army Warrant Officers. I would suggest that this is a Warrant Officers' and Sergeants' Mess photograph.
If your girlfriend's grandfather was from Eastern Europe, however, if he was Polish then it is quite possible that he was a member of the Mixed Service Organisation. The MSO was a civilian auxiliary of the post-war British Army of the Rhine, initially established to guard Displaced Persons camps, but ultimately expanded to include labourers, dog handlers, and a transport service. With the occupation of Poland by the Soviet Union in 1945, many of the two-and-a-half million Poles liberated from German concentration camps proved unwilling to return to a country where they were now regarded as politically-suspect, and remained behind to assist the British army of occupation in Germany. Many of the Royal Army Service Corps' transport squadrons in fact began life as Polish-manned MSO units before British troops replaced them, and until the 1990s, many British tank transporter operators would receive their first instruction on the vehicle from a Pole. In fact, the current 7 Regiment of the Royal Logistic Corps carries the White Eagle of Poland as its regimental insignia, in memory of the time of its heritage as 7 Tank Transporter Regiment and British Army tank transporting's connection to Poland.
Hello there! As your question is related to looking for identification/information regarding military personnel, our Guide on Military Identification may be of use to you. It provides a number of different resources, including how to request service records from a number of national agencies around the world, as well as graphical aids to assist in deciphering rank, unit, and other forms of badges or insignia. While the users here may still be able to lend you more assistance, hopefully this will provide a good place to start!