I seem to remember the survey used some pretty lose criteria - e.g. privateers, any sort of military raid counted as an invasion, provided it was with government approval. And that boundaries don't count - if the region involved in the particular conflict falls within modern boundaries, even if it didn't historically, it counts
So let's try:
- Mongolia - 19th Century. 2nd Opium War with China. British blame Sengge Rinchen for some sort of war-crime (chopping heads of missionaries or prisoners or something), chase him to Mongolia.
- Tajikistan - 1840, First Anglo-Afghan War -
Dost Mohammad Khan, flees to Tajikistan and is chased there by the British
- The vatican - 1944, Nazis put up a fight from the Vatican during the fall of Rome, British case them in
- Luxumburg - 7 years war or WW1
- Paraguey - Sir Edward Thornton manages to get Britain to send a token-force to support the the Triple Alliance during the Paraguayan War
- Krygystan - Dost Mohammad Khan again
- Ivory coast - 1940/41 over-throwing a pro-Vichy colonial regime
- Sweden - some sort of raid during the latter part of the Great Northern War - say 1717 or 1718
- Congo - easy could easily have been a British colony
- Andorra - 1940 Spain joins the Axis. In 1943, the Allies invade Spain, reaching the Pyran
- Chad - Rabih az-Zubayr ibn Fadl Allah was a powerful Sudanese warlord who established a kingdom in Chad, and was allied to the Mahdi. British take exception to him, and...
- Marshell islands - 1914, British (not the Japanese) occupy the then German islands
- Centeral african republic - can't get this one
- Monaco - 1944 British invade it to drive out Nazi occupiers
- Berundi - 1944 British invade it when its German
- Lichtenstein - 1945 British invade to capture Nazis. Lord Haw-haw flees there?
- Mali - 2012 SAS raid on Al-Q allied militants
- Uzbekistan - 1840 Dhost Mohammed again
- San tome and principe - Scientific American documented in words and pictures the continued use of slaves in São Tomé in their March 13, 1897 issue - Britain intervenes.
- Guatamala - launches attack on Belize (British Honduras) and some sort of British attack/raid/SAS-raid, etc. in retaliation or to disable the airforce etc. 1970s or 1980s would be the likely period.