Have you had a good look under the transformer, peeled back the outer winding cover?  It looks like there are 4 wires to the plug and another two white wires heading off to the left.  It is highly unlikely your transformer isn't a stock Williams factory transformer.  The secondary windings/output voltages are to unique for the transformer to be replaced with something else non original 

Yes i've peeled it all back. The white wires are secondary wires. The four wires are directly connected to the windings