I do understand, I really do.
What about buyng a pack of disposble syringes in such circumstances? They can't be that expensive surely (I believe they still come in packs of ten.)
Also, go back to your GP and order a spare set for your work and keep them there in an authorised place; there shouldn't be any issue with that, and as for keeping them at work, your employer is LEGALLY bound to make "reasonable adjustments" at your workplace (Equality Act 2010).