It is recommended that those who have had COVID-19 already should get the vaccine too. They will still be offered the jab in order of the JCVI’s priority list.
That is because natural immunity may not be long-lived and immunisation could offer more protection. Il existe des preuves préliminaires que les vaccins offrent une meilleure protection que d'avoir eu le virus. It is also sometimes difficult to know whether you have actually had COVID-19 unless you have been tested and some of the tests (such as lateral flow tests) are not always 100% accurate.
Government guidance states that there are no safety concerns in giving jabs to people with “long COVID” either. However, people who are currently unwell with COVID-19 should not receive the vaccine until they have recovered.