Hi James,
Yes some pharmacies stock Sharps containers. Also most of the public hospitals do if you are tapped into one of their programs, eg arthritis program. (They will accept full ones in ER but do not hand out new ones). Some Dr' surgeries will also, need to ask the practice nurse and she'll inform you of their procedure.
Although its not as safe, a temporary measure can be to take a plastic container that firmly seals and is waterproof that fit your used syringes. Sometimes this is easier when packing space is at a minimum. Place your used syringes in it and then on return home, tip them into the Sharps container that you ordinarily use.

Hope that helps. Cheers


MsLollyLegs