The problem may be more widespread than first considered - flame retardant chemicals are mandated for large categories of children's sleepwear. Surely direct-to-skin contact (absorption?) is at least as great a threat as off-gassing chemicals from a sofa or mattress.

If it says "KEEP AWAY FROM FIRE" in red lettering on the label, it probably doesn't have flame retardants. Though there may be false positives to this test (but no false negatives), so preferably look for something like no flame retardants.

That's completely wrong. That label has nothing to do with flame retardants. Almost all UK furniture contains FRs but there is no law at the moment that requires manufacturers to list them or even say if they use them at all.

Yes, UK furniture almost always contains flame retardants but it isn't law that they have to use them. The Furniture Regs set performance requirements but don't stipulate how you meet them. It's just that using FRs is the cheapest route to compliance for manufacturers.