There was a documentary on the choosing of the unknown warrior. Even a little bit of research would rather indicate that the soldier selected was unknown to the officer choosing the soldier and since by the time this was done the soldier would have been at least two years dead and was also placed in an unmarked coffin I'd have thought it would be nigh on impossible to know the ethnicity of the soldier. From wiki:
'Arrangements were placed in the hands of
Lord Curzon of Kedleston who prepared in committee the service and location. Suitable remains were exhumed from various battlefields and brought to the chapel at
Saint-Pol-sur-Ternoise near
Arras, France on the night of 7 November 1920. The bodies were received by the Reverend George Kendall OBE. Brigadier L.J. Wyatt and Lieutenant Colonel E.A.S. Gell of the Directorate of Graves Registration and Enquiries went into the chapel alone.
The remains were then placed in four plain coffins each covered by Union Flags: the two officers did not know from which battlefield any individual soldier had come. Brigadier Wyatt with closed eyes rested his hand on one of the coffins. The other soldiers were then taken away for reburial by Kendall.'
For a museum they really aren't very good at research.