There is nobody, ' in charge' of rescued Gypsies in the UK. Every rescue is different. Sometimes they have Gypsies in and other times, other breeds. Remember also, that most rescues, want to be able to visit, the farm or property on which their rescues will be housed. Remember it is incredibly expensive, to import horses. This will not be paid by the rescue, even if they allow a rescue out of the country.
If you were in the UK and were able to adopt a rescue, after fulfilling all the necessary requirements, it would be a whole lot easier than even trying to adopt one, to be sent abroad. Also, you would have to sign a statement, that the horse you adopt, would never be used for breeding.
I still think, your best bet is to do the homework necessary, and find someone on the European continent and purchase a horse. Importing/exporting, is no easy task. There is a ton of paperwork and reliable transportation to be done. Also there will be properly identified quarantine stations, which will be used in the different countries and according to law.
Find someone who is thoroughly knowledgeable about import/export and of course, who have well bred horses, with a known background, DNA'd to the said parents and all their ducks in a row.