This is a chunk of text taken directly from the Your Europe web site.
Please bear in mind that this information could well become inapplicable to the UK and UK prescriptions in the near future.
There may be many issues to trip us up. For example, the period of validity of any prescription may vary by country. Any pharmacy not used to handling what are to them foreign prescriptions might well wish to take extra measures to ensure they are acting legally. Make sure you allow plenty of time.
Presenting a prescription abroad
A prescription delivered by a doctor in your country is valid in all EU countries. However, a medicine prescribed in one country might not be available or it may have another name.
You can ask for your doctor to give you a prescription to use in another EU country, also known as a "cross-border prescription".
Some medicines may not be authorised for sale or may not be available in another country, even within the EU.
A prescription with the right information
There is no specific form or format for a prescription you will use in another EU country. In most cases, the prescription you would use in your home country should already contain enough information for you to use it in another EU country. It has to contain at least the following information:
Patient details: surname and first name (both written in full), and date of birth
Date of issue of the prescription
Details of the prescribing doctor: surname and first name (written in full), professional qualification, direct contact details, work address (including the country), and signature (written or digital)
Details of the prescribed product: its common name (rather than the brand name, which may be different in another country), format (tablet, solution, etc), quantity, strength and dosage.
If you think you'll need to get your prescription dispensed abroad, or if you are given a prescription abroad that you will need to get dispensed in your home country, check that the doctor has included all this information. That way you can be sure that a pharmacist in another EU country can easily understand the prescription and correctly identify the medicine you are requesting and its dose.
Prescriptions are subject to the rules of the country where they are dispensed. This means that a pharmacist will apply national rules when dispensing your medicine – for example, you may not be allowed the same number of days' dosage.
If your doctor has given you an e-prescription you need to make sure you ask for a paper copy if you plan to use the prescription in another EU country, as the e-prescription may not be recognised outside your home country.