Python: Clustering based on pairwise distance matrix
The constraints you have are not very clear (why should you start with "central items" ?). You should maybe try to come up with a well defined problem by precisely defining the clustering(s) you are looking for. 

For example, if the clustering you want is such that the maximum number of clusters is $k_{max}$ and the maximum distance between two elements in a cluster is $d_{max}$, one possible approach is to perform a Complete-linkage Hierarchical clustering of your items. Possible clusterings then correspond to cuts in the resulting dendogram. Most library include the possibility of finding a cut that correspond to $k$ clusters or at a "height" $d$. A cut at height $d_{max}$ corresponds to the smallest clustering that respect the distance constraint. If the latter is not possible with the library you are using, you can explore every cut from size $1$ to size $k_{max}$ and select one that respects the distance constraint (Note it may not always be possible to found one e.g. with  $d_{max}$ close to $0$ and $k_{max}$ close to $1$.)