  We consider generalisations of Thompson's group $V$, denoted by
$V_r(\Sigma)$, which also include the groups of Higman, Stein and Brin. It was
shown by the authors in [20] that under some mild conditions these groups and
centralisers of their finite subgroups are of type $\mathrm{F}_\infty$. Under
more general conditions we show that the groups $V_r(\Sigma)$ are finitely
generated and, under the mild conditions mentioned above, we see that they are
finitely presented and give a recipe to find explicit presentations. For the
centralisers of finite subgroups we find a suitable infinite presentation and
then apply a general procedure to shorten this presentation. In the appendix,
we give a proof of this general shortening procedure.
