According to wikipedia [0] and UK government sources [1] there are 4 countries in the United Kingdom of Great Britain and Northern Ireland: England, Scotland, Wales (together forming Great Britain) and Northern Ireland. If Scotland and Northern Ireland left the UK, it is conceivable therefore that the United Kingdom would continue to exist but as the United Kingdom of England and Wales.

[0] https://en.wikipedia.org/wiki/Countries_of_the_United_Kingdo... and https://en.wikipedia.org/wiki/United_Kingdom

[1] https://webarchive.nationalarchives.gov.uk/20080909013512/ht...