Healthcare Assistants can't write prescriptions and sign them - they may be able to write up repeats and give them to a prescriber to sign.
Nurses can only prescribe AND sign if they have undertaken a particular training programme at one of the local universities, to become a non-medical prescriber - you can tell by the prescription, in England, GP prescription pads are green and non-medical prescriber pads are purple. Pharmacists - and soon, certain allied health professionals - can write limited scrips - as can dentists - but they all have to have been throught this prescribing course (and passed it, some don't), and even then, they can only prescribe from those parts of the formulary which are in their scope of practice. Dispensaries reject prescriptions which don't meet all the criteria.
Receptionists can set up repeats but they can't sign the script.