  This paper is the second in a series devoted to the development of a rigorous
renormalisation group method for lattice field theories involving boson fields,
fermion fields, or both. The method is set within a normed algebra
$\mathcal{N}$ of functionals of the fields. In this paper, we develop a general
method---localisation---to approximate an element of $\mathcal{N}$ by a local
polynomial in the fields. From the point of view of the renormalisation group,
the construction of the local polynomial corresponding to $F$ in $\mathcal{N}$
amounts to the extraction of the relevant and marginal parts of $F$. We prove
estimates relating $F$ and its corresponding local polynomial, in terms of the
$T_{\phi}$ semi-norm introduced in part I of the series.
