If you are going to buy a cheap mountain bike?

An mtb is fine for a short commute. I do think there's a significant difference in speed going to a CX or road bike, maybe 1-2mph or so from personal experience, but it isn't massive and as others have said, it will deal with poor roads very well. Some people like the upright position for keeping an eye on traffic around you too.

Unless you like to haul the bars around while stomping on the pedals, (ie so long as you have a relatively smooth style) fork lockout isn't critical. I very rarely use mine, even on road. What is important is that any suspension fork has hydraulic (oil) damping. I'm not sure if it's still the case but a couple of years back many entry level MTBs came with dreadful forks with no damping. Those were truly awful and bounce around all over the place, especially when on the road. I think more bikes have a proper damped fork now though.

Nat Has Moe is correct, it's the engine, you won't lose any appreciable time commuting on a MTB over average distances. I stayed ahead of a speedy roadie tonight for a bit, was quite fun on my Cannondale SL3.

They're much better in winter due to better rigidity and wider tyres, and more of a 'take-everything-the-World-throws-at-it' type of build. Pop some semi-slicks on and job's a good-un. If your journey has lots of rough surfaces then a touch of a decent suspension can make the commute a more pleasant and fun experience.

All that said, I may swap to cyclo-cross next year...

I also used to commute on a MTB. it was fitted with slicks and to be honest I could go faster than some commuters on all carbon road bikes. Its not the bike that makes you fast, its your engine. By the way the MTB was a very heavy aluminium downhill full suspension bike. So the MTB could be the jobbie for you.

I used to commute on my MTB without any problems. Lock out the front forks, fitted some slick tyres and it was fine.

The hydraulic brakes saved me on a couple of occasions from dangerous London drivers, it may not be the best choice for a commuting bike, but it will certainly do the job.

You don't need suspension to ride offroad, a cheap bouncy fork is worse than nothing.

A hybrid or traditional sit-up-and-beg bike would make a better option for a commuting/town/general bike. If you want it to be cheap (and low maintenance) then keep it simple - no fancy hydro brakes, no suspension etc., preferably singlespeed, ideally with a chainguard.

^Yep if you're going to dual purpose or you want a new bike it find something with a hydro lock-out fork and hydro disc brakes. The Giant Talon looks like a decent option. For strict commuter duty, something cheap and second hand with a rigid fork and some Schwalbe Big Apples or similar is a very smooth if somewhat slow (but that means maybe a couple extra minutes in a 20 minute commute) option.

With the right tyres a RIGID mountain bike will make a perfect commuter and will effectively be a "hybrid" but with better tyre clearance.
You don't need 700C wheels and narrow tyres to go fast.
If you know what to look for you could start with a nice rigid retro MTB for £150-250 off EBay.

Why would you want a mountain bike to commute? Unless you have a lot of offroad riding it's just a lot of weight and draggy tyres to cart about. Otherwise, a hybrid is much better, with no suspension fork.