Compatibility summary
You will need a travel adapter in Christmas Island; plug types used there differ from United Kingdom.
Plug comparison
United Kingdom plug types: G
Christmas Island plug types: I
There is no common plug type between United Kingdom (G) and Christmas Island (I). You need a travel adapter.
Voltage comparison
United Kingdom: 230V, 50Hz
Christmas Island: 230V, 50Hz
Voltage difference is within a range many devices tolerate; check your appliance label.