DendogramPlot accepts Axes as an option.
For various combinations of DistanceFunction and Linkage you get the following pictures:
{#, DendrogramPlot[{1, 2, 10, 4, 8},
DistanceFunction -> Automatic, Linkage -> #,
Axes -> {False, True}],
DendrogramPlot[{1, 2, 10, 4, 8},
DistanceFunction -> ManhattanDistance, Linkage -> #,
Axes -> {False, True}]} & /@
{"Single", "Average", "Complete", "WeightedAverage", "Centroid", "Median", "Ward"} //
Grid[Prepend[#, {"", "EuclideanDistance", "ManhattanDistance"}],
Dividers -> All] &
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}]
