New bike advice - Singlespeed/fixed, mountain, or road I'm looking at getting a new bike to replace my current hardtail mtb for commuting about 8 miles a day, plus possible train travel, and longer commutes elsewhere. 

With a budget of under £400, do I go for a mid range singlespeed/fixie with a flip flop hub, and just man up and struggle through the hills, or get a bottom/low range road bike, risk it getting stolen/trampled/damaged, but have the ability to go on longer rides (which doesn't really interest me, but will still happen occasionally). 

As I see it, a singlespeed is less flashy, so therefore will not attract as much attention with regard to theft, and although would be a struggle on longer pleasure rides, will outweigh the benefits of a road bike with gears?
There are only really two things. First, as you identify, there is the issue of gradients. If you think that difference goes away if you just "man up", good luck with that. Even if you had the leg power (most of us don't, we'd end up pushing the bike and likely mashing our knees in the process), it would be very difficult to select one gearing that would be suitable for all gradients.

The second thing is maintenance. Single speeds are a bit easier to maintain because there is no derailleur arrangement. Get your chainline right and you're basically down to fixing punctures. So if you're not into diy, or money will be tight as regards keeping the bike on the road, then that could be a factor. But you still have tyres, brakes and less frequently bottom brackets and chainrings to worry about, just like a road bike.

I think your reasoning about theft is likely wrong, or at the very least governed by geography. I can imagine certain places where it is ultra-cool to ride a fixie, and therefore they would be in strong demand. For example, London, Tokyo, probably other cities too. I mean, these things are largely fashion accessories. Also I think buying a bike because it is less likely to get stolen is a recipe for disaster (especially when it gets stolen).

I think you're right in terms of your price analysis though. In the "new" market, a budget of £400 will not buy a good road bike. You might have a chance of finding something if you're wanting a flip-flop, although my flip-flop (a nothing-special Charge Plug) retailed new at around £600 iirc. Secondhand gives you more scope, of course (I got mine off eBay), but you need to know what you're looking for.

You mention mountain bikes in the title, but not really in the question. The pros/cons of these are pretty much the same as the pros/cons for road bikes, in this context at any rate.