Should I learn to use LaTeX to write up a History Masters Thesis?

I'm finishing up a PhD in philosophy that I've written in LaTeX. Here's some suggestions:

• make sure your advisor is ok with leaving you comments in pdf. I suspect he or she will not understand the question and will not be able to give you any feedback unless you submit chapters in word format. This is a deal breaker. Don't make any more problems communicating with your advisor than absolutely necessary.
• lots of academic journals in the humanities still don't accept submissions in pdf or latex source form. If you are planning on submitting your stuff to a journal, you might save yourself time writing in word format.
• there are some tools available to convert latex to rtf, html and other tools. texht is the best.
• If you do decide to go LaTeX, don't get lost in the minutiae of learning how to tweak everything. It's easy to lose lots of time learning new packages and stuff when you should be writing, writing, writing. Use the wikibooks latex guide as your quick start guide when you need to learn how to do something fast.
• Especially if you're on Ubuntu, don't get the LaTeX distributed through Canonical's repositories. It's usually out of date (haven't checked in a while). Just go on and get the vanilla TexLive 2013 distribution from CTAN.
• The tex.SE site is really, really good. Like ridiculously helpful.
• If you are familiar with version control programs like git, mercurial, or svn you can actually keep a very precise idea of exactly how your thesis has grown over time. You can roll back changes, etc. This is kind of advanced stuff for LaTeX, so I wouldn't spend like a lot of time learning this stuff if you aren't already familiar with it, but if you are, it can be really helpful. EDIT: Per @henry's comment below, see the following guide by Roger Dudler to get started with git.

When my husband did his master's, he used LaTeX to write his thesis even though his supervisor preferred Word and everyone else in his lab used Word. He encountered some pros and cons.

Pros of using LaTeX:

• Word gets very slow and buggy once your documents are past a certain length, say forty or fifty pages. One of my husband's friends spent a day renumbering all of the figures in his thesis after the numbers mysteriously disappeared. I'm not sure if this issue exists with LibreOffice, but it may.
• You mentioned breaking your thesis into smaller documents and combining them later. This is easily and commonly done with LaTeX; it would be considerably harder with LibreOffice. [Edit: derobert pointed out that LibreOffice supports this through a "master document" feature. I wasn't familiar with it.]
• It's much easier to change the formatting of the document at the last minute if you discover that, e.g., your margins don't match your university's specifications or your references are formatted incorrectly. It's also easier to keep the formatting consistent.
• The results are more aesthetically pleasing, if you care about things like ligatures and kerning.

Cons of using LaTeX:

• LaTeX has a much steeper learning curve, as others have mentioned. If you don't need to use it after you're done your thesis, it may not be worth the time investment.
• LaTeX forces a slightly different editing workflow since you can't turn on Track Changes. Your supervisor will have to mark up the PDFs you produce or add comments to the tex file itself. This may make your supervisor less happy about your choice.

My recommendation: use LaTeX to write up something short that you need to write anyway to see how it works. Then play around with some of the features you'll need for a thesis: add a footnote, a reference, or a figure. Try the \include command, too. That should give you a sense of whether it's something you want to continue with.

I'm sure how familiarity or usage of LaTeX within the History department will impact on my decision but would also like to prepare my thesis in the best possible way.

I would say that it should impact your decision strongly. You should prefer a tool that is used by your colleagues and supervisor to one that is slightly better intrinsically. They are the people who know what you need to do, and how to accomplish it with the tools they know.

I personally prefer LaTeX to LibreOffice, but I would guess that the combination of LibreOffice and Mendeley have all the features you need. (One in particular that I'm going to call out is change-tracking. Enable it as soon as you start, or you'll wish you had before long.) But the advantage of knowing your tool and having colleagues who know your tool outweigh most of LaTeX's advantages.