English and Welsh aren't nationalities. Your nationality is British, under the British Nationality Act.
That's the legal point of view, as far as I'm aware as a non-lawyer anyway.
You can say whatever you want though. People have all these crazy ideas saying they're half Welsh, half English; some of the weirder ones include being one third Irish, one third Spanish and one third English; or even one quarter French, one quarter German, one half British.