Ivy Katy they'll just use the same sample.
So no real science involved then, eh ? If that's the level of evidence required they may as well have asked the local clairvoyant what their spirit guide told them ... (looks like I missed a cowboy trade I could have raked it in from there ...)
If they were serious about drug testing (which they clearly aren't) they'd have matched the police procedure for dealing with suspected drug drivers, and started with a mouth swab. In the event that was positive they would proceed to a blood sample. Or indeed, if it was negative (but let's not dwell on that). But, as noted upthread, such tests cost money.
Call me cynical, or call me someone that's worked in a lot of places, but if I had a budget of fuck all, and I wanted to pretend I was enforcing a (I bet the OPs firm is ultimately run by a US company - they are obsessed with drugs to an unhealthy degree) workplace drugs policy, then I would conduct a urine sample pantomime, and wait for the inevitable 5% to raise their own hand for the chop.
Incidentally was there any warning before they pulled to you one side that they would be conducting a random test ? (You need to look deep into your contract to make sure they followed their own guidelines).
If the OP is still worried, then they should consider looking elsewhere for advice ... there's a whole UK community out there with hundreds of thousands of person-hours of experience in dealing with these things.