A Licensed Marriage and Family Therapist is an American credential for therapists trained specifically in working with couples and families, although in practice most LMFTs also see individual clients as part of a broader caseload.
Training that treats difficulties as patterns between people
Requirements include a master's or doctoral degree specifically in marriage and family therapy, supervised clinical hours working directly with couples and families rather than individuals alone, and a licensing examination. The training itself is systemic in nature, treating difficulties as patterns that exist between people rather than problems located inside a single individual, which shapes how an LMFT approaches even individual client work.
The nearest UK equivalents
This is an American credential and does not transfer to UK practice. The nearest UK equivalent is the family and systemic psychotherapist registered with UKCP, whose training shares the same systemic underlying philosophy, while couple therapists registered with BACP or COSRT cover a good deal of the same practical ground for people specifically seeking help with a relationship.