DendogramPlot accepts Axes as an option.
Inter-cluster distances in a Cluster object are given as the third from last element.
In the following, these distances are highlighted in red:
Grid[{{Agglomerate[{1, 2, 10, 4, 8},
DistanceFunction -> Automatic,
Linkage -> "Single"]},
{DendrogramPlot[{1, 2, 10, 4, 8},
DistanceFunction -> Automatic, Linkage -> "Single",
LeafLabels -> (# &), ImageSize -> 300, Axes -> {False, True},
AxesOrigin -> {0, Automatic}]}}]
So ... this verifies that vertical axis does indeed measure the inter-cluster distances for a given DistanceFunction and Linkage.
For various combinations of DistanceFunction and Linkage you get the following pictures:
{#, Agglomerate[{1, 2, 10, 4, 8}, DistanceFunction -> Automatic, Linkage -> #],
DendrogramPlot[{1, 2, 10, 4, 8},
DistanceFunction -> Automatic, Linkage -> #,
Axes -> {False, True}, AxesOrigin -> {-1, Automatic}],
Agglomerate[{1, 2, 10, 4, 8}, DistanceFunction -> ManhattanDistance, Linkage -> #],
DendrogramPlot[{1, 2, 10, 4, 8},
DistanceFunction -> ManhattanDistance, Linkage -> #,
Axes -> {False, True}, AxesOrigin -> {-1, Automatic}]} & /@
{"Single", "Average","Complete", "WeightedAverage", "Centroid", "Median","Ward"} //
Grid[Prepend[#, {"", "EuclideanDistance-Clusters",
"EuclideanDistance-Dendogram", "ManhattanDistance-Clusters",
"ManhattanDistance-Dendogram"}],
Dividers -> All, Alignment -> Bottom] &
EDIT: Note: Despite syntax highlighting in red of Axes and AxesOrigin, the options seem to work:
DendrogramPlot[Prime[#] & /@ Range[30], Axes -> {False, True},
AxesOrigin -> {-1, Automatic}]
