There isn't a set list of GCSEs you *need* to become a linguist. University entry requirements vary, but generally, strong grades in
English Language and at least
one other language are highly advantageous. Further maths, or just maths itself, can be useful depending on the specific area of linguistics you pursue (computational linguistics, for example, often benefits from a strong maths background). Beyond that, a broad range of GCSEs demonstrating academic ability is generally welcomed.
It's the A-Levels or equivalent that are more critical for university applications to linguistics degrees. Good grades in English Language, a foreign language, and perhaps a subject like History, Philosophy or Psychology are often favoured.