Thank you both for your help. Safety is key for me and something I do my best to take seriously (though none of these will be used by anyone but me!), but I'm also hampered by not having much in the way of funds to spend on them. Rewiring them myself was in the hope of saving money (they were free). So until I can get them PAT tested I'd settle for reducing the risk and not having to work in the dark.
On a worrying note...I got one of the lamps off a family member and opened the plug to discover the earth wasn't connected. She'd been using it for years.