The Joint Nature Conservation Committee is out with a report on "Non-native species in UK Overseas Territories." The review looked at non-native plant and animal introductions on 17 different British Overseas Territories (Bermuda, Falkland Islands, etc.) and the Crown Dependencies (Isle of Man et al.). More than 2200 different species introductions have been recorded in the survey areas, and the researchers note that is most likely an underestimate, since few of the territories have completed full inventories.
There don't appear to be a lot of similarities between territories, with the number of non-native species ranging from over 1000 (Bermuda) to none or close to none in some cases. Species found in four or more territories include standard island pests like feral cats (felis catus) and black and Norwegian rats (Rattus rattus and R. norvegicus), and also the red imported fire ant (Solenopsis invicta), ice plant (Carpobrotus edulis), and mesquite (Prosopis juliflora).
At the bottom of the page are links to the full report here (.pdf) and the complete data set in an Excel spreadsheet (.zip). Note that the report is about non-native introductions, with no determination made as to whether the species found were "invasive" or not. It is also not clear whether species had to be naturalized to be included in the study.