In terms of pop music of the 21st century two British invasions occurred. That happened twice, when single artists or brand from Great Britain ruled the music charts of other countries, especially the USA, and scored one number one hit after the other over months and years.
The first British invasion
The first took place between the late 1950s to the early 1970s, when band like The Beatles, The Rolling Stones, Pink Floyd, Queen, The Who, Led Zeppelin, single music artists like Elton John, Eric Clapton, Phil Collins, od Stewart and others were on the top of the music charts of many countries, not only in the UK. They moved local bands and artists to lower places, depriving them to reach the number one position of their respective chart. Audiences, especially teenagers, went mad and bought more records than of local acts.
The second British invasion
Between the late 1970s and mid 1980s was the era, when the second British invasion took place. Its focus was on synth pop, which emerged around that time. Acts like Gary Numan, Depeche Mode, OMD, Yazoo (known as Yaz in the USA), The Human League hit the number one spot also in charts outside the UK. Local artists were again moved to lower chart positions. Interestingly, while the first invasion was focused on Rock, the second invasion with focus on synth pop also created several new music genres, like New Romantic Wave, New Wave, Ska. And opened the way to cyber punk while competing with Disco Music. This invasion fizzled out around 1983, when American musicians were again able to rule the charts of many countries.
Looking back I miss that time of the second invasion. I was a teenager back then and loved to listen to the radio while recording the songs to create mixed tapes (on compact cassettes, kids today won't know). I doubt that there will ever be a third British invasion again.