EU to UK license

Hello lovely people! i need your advice on license exchange. i lost my EU license, which i wanted to exchange for UK anyway. do i need to reapply for my EU license to do so? which would obviously take more time and double the expenses.
i spoke to the license agency in my country and they said that DVLA contacts them to confirm the provided info anyway; and they could supply me with some sort of proof that i do hold the license. would that be enough? i could not find any info on that on DVLA page and different forums say different things. does anyone have any actual experience in this?