Can I go to England with my EU family member ID card?

As someone who is not a citizen of the EU, a national of an eea country, or a citizen of Switzerland, you need at least a passport to enter the UK (although if you are a refugee or stateless person, this could also be a passport-like document issued to you by your country of refuge).

If you are a national of a visa-exempt country, you do not need any document other than your passport.

If you are not a national of a visa-exempt country, you may nonetheless be exempt from the visa requirement, under the conditions described by the Maltese authorities, if you hold an Article 10 residence card. Your card does not appear to be an Article 10 card, however, since the Maltese version of Article 10 says that such a card should include the text "Karta ta' residenza ta' membru ta' familja ta?-?ittadin ta' l-Unjoni," which is absent from your card. Your other question indicates that your wife is Maltese, so it is to be expected that your card is not an Article 10 card.

This leaves you with the visa requirement. If your spouse is an EU citizen (as your other question indicates) and you're traveling together, you can get an EEA family permit, which is free of charge and should be issued quickly.

If your children are the only EU-citizen members of your family, you will most likely be unable to derive free movement rights from them, in which case you will need a standard visitor visa. Your other question suggests that this is not the case.

International travel requires a "travel document," such as a passport (which reflects the holder's citizenship or nationality), or a refugee travel document (which reflects a country's acknowledgment that the holder is a refugee now resident in the country that issued the document. Both of these documents identify the holder.

In addition, depending on which country issued the travel document and which country is the destination, the traveler may also be required to have already obtained a visa (that is, permission to enter) from the destination country.

The document pictured in the question appears to be a permit to live in Malta. While this document may affirm the holder's right to live in Malta, it falls short of qualifying as a Refugee Travel Document as it not in passport-like booklet form as required by the Convention Relating to the Status of Refugees, which includes data about the holder and a photograph.

Because airlines are responsible to return refused-entry travelers to the airport from which their flight departed, and such returns cost money, airline staff checks each embarking passenger's documentation before the passenger is allowed to board the aircraft. If a passenger's documents are not sufficient, the passenger will not be permitted to board the flight.

Thus, you will most likely be denied boarding on any flight terminating in the United Kingdom. If the airline does allow you to board, you will be refused entry by UK Immigration.

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Edit: my answer above, while a correct statement of general travel practice, is inapplicable because the OP has indicated in another SE Travel question that his partner and child are Maltese passport holders. @phoog's answer reflects the OP's situation, and is more accurate.