I am about to self-release a book. I am looking for a publishing house
that can handle the layout work involved in this, yet also will
present me with however many copies of the book I want. All of the
publishing houses I have found on the internet do the layout work,
etc, for you - yet will only sell you copies of your book at wholesale
cost. I would like to have the company print my book to my specs and
then deliver me 200 copies of it. Can you help me find a company that
can do this?

You don't need a publishing house, as you are doing your own
publishing. You need a typesetter for the layout work, and a printer
and finisher (bookbinder) for the actual production.

200 copies however is an extremely short run and will probably be
rather expensive on a cost per copy basis.

Your local university probably knows of finishers who handle short run
binding  of theses and course texts.

Owain