At the risk of sounding controversial where no controversy exists, i would respectfully suggest there was a literary relationship between Heaney's practice and Larkin's. Heaney wrote, not without reservations, about Larkin several times in prose, but most memorably in 'The Journey Back', the opening poem of 'Seeing Things', which though deftly written also conjures the strange comparison of Larkin to Dante, representing as it does a supernal vision of Larkin's shade a la Dante's appearance to firewarden TSE.
Larkin himself made some not entirely flattering comments on Heaney, a 'Gombeen man' being the most notorious, but most pointedly suggested that 'Heaney &co.' represented a retreat to the 'literary'. I think he says in a letter that they 'where we were when we first started out'.
Perhaps I could not so respectfully suggest that, rather than 'neo-Movement' and the like, the term 'neo-Georgian' be employed, as did Spender in his c.1960 attack on Larkin, Hughes etc.I don't think it entirely satisfactory, nor do I entirely condemn the 'Georgian' poets, who were really a series of anthologies anyway, rather than a literary movement, but the key element of critque is also I recall right also summed up by Spender: 'cultivating their own back gardens' - in literary terms that is.
I also recall US American critics applying it some of their own post 1960s generation, though at this distance in time I'm not sure of whom.