if you buy a new table lamp from B&Q you’ll probably find that only the live & neutral are wired anyway.
from recent experience (been there 4 times since March, going again tomorrow am) Ireland has the same 13A square pin plugs as UK so if it was a 2 pin plug, it was probably a shaver type plug and a shaver adaptor plug would have been fine.
but now you’ve cut it off, you should be able to simply fit a standard UK plug. bRown – Right, bLue – Left*.
*disclaimer for numpties.
This is with the plug viewed from above with the cable going in at the bottom. If you’ve got it rotated so that the cable is not going in at the bottom, rotate it until it is, then the Right/Left rule applies. Not that it really matters for a table lamp, not exactly directional is it?