I usually get stuff like that on ebay.co.uk. (not all second hand stuff there by anymeans) Delivery is generally 2 to 5 weeks so there is no time to lose. I just searched "union jack t shirts and got more than 6000 items! (this particular one is more dress than tee shirt:
http://www.ebay.co.uk/itm/Union-Jack-Dress-Spice-Girls-Dress-Back-Stock-...

Alternatively - if it helps, I have a union jack about 500mm x 500mm (printed just one side - mabe intended as a handkerchief or tea towel. Its new, perfect and free if you want it. It could easily be stitched on to a white tee shirt