I don't think so. Most of the time "Britain", "Great Britain" (GB) and "United Kingdom" (UK) are all just different ways of abbreviating the cumbersome expression "United Kingdom of Great Britain and Northern Ireland".
"Britain" can also refer to the island comprising (today's) England, Scotland and Wales. I think it would be somewhat unusual to use the expression "Great Britain" to refer to the island: Julius Caesar arriving in "Great Britain"? I don't think so. That would be "Britain".