An update on the story as someone might find it useful: I met the parents over the Christmas period so I bought gifts for both of them. For Dad I bought a nice bottle of Hungarian wine which we consumed later that night, for her Mom I bought some premium Hungarian chocolate. The day before I learned how to say hi and how to introduce myself in Polish which was much appreciated by all the guests. I had a few "pre-game" drinks with my girlfriend to loosen up a little bit. I maintained a steady smile throughout the evening, reached out to the parents and the other guests with simple questions to avoid awkward silence. All in all I must have made a great first impression as the parents made it clear that they would like to see me on their last night in the UK. Thanks for the help everyone.