There are around 200,000 migrant Roma in the UK, with another 200-300,000 people who meet the broader Council of Europe definition of "Roma". Irish travellers are the main other itinerant group; estimates suggest that there are around 25,000 Irish travellers in the UK.

All of this data is fairly vague, because itinerant people are inherently difficult to survey. There is only a single census category for "gypsy/traveller", so that's of little help. Many indigenous British travellers do not identify themselves as being Roma and have unclear origins, further complicating the situation.

http://www.salford.ac.uk/__data/assets/pdf_file/0004/363118/... http://itmtrav.ie/irishtravellers