The transition of the old British VR1, VR3 and VR8 into the current T2 and T3# prefixes is a little complicated.
There is an article in the San Diego DX Club Bulletin for July, 2011 which explains the history quite well.
Please see http://www.sddxc.org/bulletin/2011/July-11.pdf and start reading at the paragraph before the heading "How VR1 and VR3 Became VR8, T2, T3Ø, T31, T32 and T33".
Further information: DXNS #882, dated 1979-10-03, published by Geoff Watts, reports:
"T3 - the former Gilbert Islands Colony is now independent Kiribati, but as it still comprises the Gilbert Is & Ocean I, Christmas, Fanning & Washington I, Phoenix Is, there is no change as far as DXCC is concerned. It is reported : VR1A- is now T3K-,VR1P- & VR3 will be T3P & T3L".
Club Log maps the T3# prefixes to the appropriate entity from 1979-10-01.
Thanks are due to the San Diego DX Club.