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You need to be able to present a marriage certificate together with this article 10 residence card (that's the same thing than the βresidence card for a family member of an union citizenβ you asked about with respect to Ireland). Even if it's not very clearly written, that's what the Wikipedia text means and the official gov.uk website is very clear about it.
So you cannot (easily) reach and enter the UK with the marriage certificate only. If you don't have the right type of residence card, you are supposed to get a visa (see also Will a non-EU citizen get stamped with a family permit at the airport?).