Yes. The Isle of Wight lies 2–5 miles off the Hampshire coast in the Solent, making it geographically part of the island of Great Britain (the landmass comprising England, Scotland, and Wales).
It's a ceremonial county and a unitary authority (Isle of Wight Council), separate from Hampshire since 1995. It has its own Lord Lieutenant and High Sheriff.
The Isle of Wight is part of both—it's on the island of Great Britain and within the UK.
Channel Islands (Jersey, Guernsey) – Crown Dependencies, not part of Great Britain or the UK.
Isle of Man – Also a Crown Dependency, in the Irish Sea.
So if you're standing on the Isle of Wight, you're on British soil in every geographic and political sense.