You do have some control over this.
Say I have a simple chart:
Look at the Chart -> Chart Areas property:
You can control the position of items in the chart with the various CustomInnerPlotPosition and CustomPosition values.
These are all disabled by default:
However, you can enable and change to control the chart rendering:
Here I set CustomPosition -> Left to 0.
Default properties:
Updated properties:
You can see this has reduced the whitespace. Depends on your chart, but maybe this will be enough.
Read more at Fit Chart Labels Perfectly in Reporting Services.