This paper is the second in a series started by [Ignacio L. López Franco, Formal Hopf algebra theory I: Hopf modules for pseudomonoids, J. Pure Appl. Algebra 213 (2009) 1046–1063], aiming to extend the basic theory of Hopf algebras to the context of pseudomonoids in monoidal bicategories. This article concentrates on the notion of lax centre of a pseudomonoid and its relationship with the Drinfel’d or quantum double of a finite Hopf algebra and the centre of a monoidal category. We can distinguish two parts in the present paper. In the first, for a pseudomonoid A with lax centre Z ℓ A in a Gray monoid ℳ with certain extra properties, we exhibit an equivalence ℳ ( I , Z ℓ A ) ≃ Z ℓ ( ℳ ( I , A ) ) of categories enriched in ℳ ( I , I ) . In the second, we construct the lax centre of a left autonomous map pseudomonoid A as an Eilenberg–Moore object for a certain opmonoidal monad on A . Moreover, if A is also right autonomous, the lax centre coincides with the centre. As an application, we show that a (left) autonomous monoidal V -category has a (lax) centre in V - Mod , of which we give an explicit description. In another application, we prove that a finite-dimensional coquasi-Hopf algebra H has a centre in the monoidal bicategory Comod ( Vect ) and it is equivalent to the Drinfel’d double D ( H ) .