Dommie '53, Front Rim

To get a replacement rim, you don't need a part number as such. look in your riders handbook for the rim size. Probably WM1 or WM2 x19.  That's what counts.
With any luck that info is marked on the edge of the rim. Your tyre size confirms what it's diameter is.

To order a rim, someone like Central wheels will need to know the hub size (7") as well as the number of spokes and the diameter of the other side if it's not a full width hub.

Try them,  ( or any other motorbike rim supplier ), they will assist.