I wasn't aware that there was a priority service for EEA family permits.
You should also note that priority service is not usually available if you have had a refusal in the past in the past.
https://www.vfsglobal.co.uk/co/en/premi ... ority-visa
How long does it take to get a visa?
UK Visas and Immigration aims to make a decision on your Priority Visa application, and contact you to let you know that your passport is ready to be collected within 5 working days from when you submit your biometric information.
However, every application is unique, and if your application is not straightforward, it may not be possible to meet this timescale. If this is the case, your application will still be put at the front of the queue at every stage of the decision-making process, and UK Visas and Immigration will aim to process your application within global customer service standards. Your application may not be straightforward if you have:
been refused a visa for the UK, and/or;
been refused leave to enter the UK, and/or;
been deported, removed, or otherwise required to leave the UK, and/or;
overstayed a period of leave in the UK, and/or;
had leave to remain in the UK curtailed by the Home Office, and/or;
been refused leave to remain in the UK by the Home Office, and/or;
been refused a visa for Australia, Canada, New Zealand, the United States of America, or the Schengen countries, and/or;
you have been interviewed, detained, or prosecuted by the police for any offence in the UK or elsewhere, and/or;
you have an unspent criminal conviction in any country, and/or;
you have committed a criminal offence in any country
If you fall into one of these categories, you may not want to use the Priority Visa service, as UK Visas & Immigration may be unable to process your application within the 5-day timescale.