1. Dear Martin, the important point you need to be aware of is that your Croatian national wife will not need a visa in order to live and work in the UK because she is the spouse of you, an EEA national. So your wife can live and work in the UK without restriction. To prove her right to work, she can apply for a Blue Registration certificate and this she can show to employers to prove her right to work. A blue registration certificate costs GBP 65. Here is a link to the UK Government website which sets out the position and has an link to the application form. https://www.gov.uk/croatian-national/family-members
2. Be aware that this is the position because Croatia is now a full member of the EU. So the restrictions are limited.
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4. As I mentioned in my earlier answer, the Blue Certificate is merely proof to show an employer that your girlfriend can work. It is not essential. This is mentioned in my earlier answer and is set out in the piece from the UK Government website to which I have referred you.
5. So, there is no impediment to her immediately starting to work for this employer. There are no legal obstacles and they aren't breaking any law. Again refer to the piece from the Uk Government website to which I have referred you.
6. Ultimately, be aware that the Home Office aren't engaged in the provision of information. So, if her employer had difficulty in getting this information from the Home Office it is merely because this is not their function.
7. Dear Martin, if you read the bit I referenced to you under "Purple certificate" and where it says "
"When you won’t need a purple certificate
You don’t have to apply if you:
8. Finally, if you aren't happy with what I have given you and still cannot find it, I would suggest you hire a solicitor to formally write to your girlfriend's employer and point out the legal situation to them. This is my final recommendation if you still cannot find what you are looking for.