Derailleur hanger built-in/cast with frame — options if misaligned? As per the photos below showing visible misalignment of the rear derailleur hanger:



and secondly its construction (where it is built-in with the dropout and frame):



Please could you help me and describe options to repair this bent hanger? 

I suspect a hanger alignment tool is only meant for use with a 'replaceable hanger'?

Thank you so much for all and any help.
This looks to be a steel frame which has a steel derailleur hanger. Steel is much more ductile than e.g. aluminum alloys and it can be bent/realigned (reasonably) many times before it cracks.

So don't be afraid to use an alignment tool if you have one. If you don't have one, use an adjustable spanner wrench to grab the hanger and align it. Even if it is steel, be careful and do not over-bend it.

Even if the worst happens and a crack develops or the hanger falls apart, it still can often be fixed by welding, but that would be much more involved and expensive, so try to avoid that of course.


  I suspect a hanger alignment tool is only meant for use with a 'replaceable hanger'?


Not really. In fact, replaceable hangers are mostly made of aluminum alloy which is more brittle than steel and survive less realignment attempts than fixed steel ones.