Hi,
I have been very curious about the label so have been doing a little more delving but not sure what I have will help or you may already know.
Much of the Dickies short sleeve workwear I have viewed have two breast pockets not one which is what made me think the shirts might be part of their Scrubs Workwear.
I could not originally find anything that remotely looked like the label logo and colours used.
You will already be aware of their standard colours in their logos/labels although I did find a couple of variations.
Also, most of the short sleeve shirts have two labels, the other attached to a sleeve or bottom of shirt but again standard colours.
I did trawl through eBay and found a couple of Dickies Shirts whose labels came damn close, White/Blue but no other information to be had.
However a little more perseverance and if legit, I think your shirts were made in Portugal or Bulgaria and not for the UK market, 80s into 90s
This info came from Dickies themselves.
Lastly and I didn't know this, while Dickies clothing is still available most places, if I understand correctly, from the manufacturing side of things they have all but shut shop at least in Europe.