If your budget is tight, then you're probably best off keeping what you have. Beyond switching to slick/semi-slick tires the actual performance gains drop off pretty fast. Ride the bike you have a lot and you'll get stronger, then when you can afford a road bike you'll really fly.

If you had some spare money, the biggest opportunities for gain I see would be replacing the suspension fork with a rigid fork. Suspension forks, especially those lacking lock out, soak up a certain amount of your energy with every pedal stroke. Replacing that probably wouldn't actually make the bike much faster, but it would feel a lot faster. The trick is to find a fork that matches the the length of your suspension fork without changing the geometry of the bike. It's likely to make your bike look a little goofy anyway, but the important thing is to keep the riding position and handling correct. If you could do the work yourself to replace the fork, you could probably do it for under £75 (assuming you can get a basic steel fork as cheaply there as we can here in the U.S.). Off the top of my head, I think you could do the work with one or two hex wrenches (which you ought to have anyway) to adjust the stem and headset, a piece of PVC pipe and a hammer to install a new crown race, and a hacksaw to cut the steerer to size. Obviously we're talking about a lot less bang for the buck than you got with the tire upgrade, but it's probably the best thing left short of a whole new bike.