I eventually created a tool at work to do this and thought I would share it if anyone is interested. It is pretty simple as I am not a programmer. The script will make a list of all rasters in the input workspace and clip them to an input feature class. Each output raster will be named the same as the original raster plus "_Clip".
import arcpy
#Set variables
wspace = arcpy.GetParameterAsText (0)
clip_feature = arcpy.GetParameterAsText (1)
#Set user input workspace (Geodatabase containing rasters)
#and output cell size
arcpy.env.workspace = wspace
arcpy.env.cellSize = 30
#List rasters in the workspace and clip them to the user input feature class boundary
rlist = arcpy.ListRasters ()
print rlist
#The output name will be the input raster name followed with "_Clip"
name = "Clip"
for rast in rlist:
arcpy.Clip_management (rast, "#", rast + "_" + str (name), clip_feature, "", "ClippingGeometry")
This could be brought into model builder if required as another solution to my own question.