Taken from BA website.
Please be advised if you are carrying any of the above items (with the exception of hypodermic needles when proven to have a medical need for it/them) will be asked to place it in their hold baggage/suitcase. If you only have hand baggage then you will be asked to hand over the restricted item for disposal by British Airways.
Note: Tweezers, nail clippers, safety pins and sewing needles up to 2 inches in length are permitted in hand baggage.
Also everybody for information the following,
Virgin Atlantic site...
If you have a medical reason that means you need to inject during the flight you are permitted to carry syringes in the cabin. But you might be asked to produce medical evidence such as a doctor’s letter when you check in or at security screening. The letter should be kept with you at all times.
Easyjet...
The following items are not permitted to be taken into the cabin, and will only be accepted if packed securely in hold baggage...
Hypodermic syringes (unless supported by medical evidence)
Ryanair...
MEDICAL SYRINGES
If for medical reasons, passengers need to inject themselves during the flight (e.g diabetics) they are permitted to carry syringes in the cabin. They will be asked to produce appropriate medical evidence (a doctor’s letter will suffice) when they check in or at security screenings. This should be kept with them at all times.
It's fairly clear you need medical evidence to travel with these airlines, though some airlines it wasn't, I couldn't find info at BMI or Cathay Pacific. Also the TSA don't require written evidence they just need to see the syringes and medication. So it's not the case with all airlines, or at least they don't give any information that they do require medical evidence.