iflogit- if you're riding on dirt and stone tracks try and keep things simple. Go for a basic but lightweight bike, rather than upgrading a basic bike that has an Altus spec. If you can stretch to about £500 this will get you a wonderful bike that'll do all you need and more should you get further into it.
I'd say in this situation, buy new and buy from a local shop. That way they're always there to help you out when you need advice- you'll (generally) get much clearer advice from a shop than an internet forum, and if you can show them much wrong they can avoid baffling technical descriptions to help sort it out, rather than describing it on the internet.
Upgrading a basic bike like yours has its negatives and positives. On the plus side, it's cheaper than a new bike. On the down side, to get it to a really nice spec it'll be better value to get an all new bike. A lot of places will do trade ins, and if not you can sell yours on ebay or a similar site.
In a new bike, look for 8 or 9 speed gears and forks from a reputable brand- the best ones to look for around £500 are called Rock Shox Darts. They have around 4" of suspension travel and usually have a lock that turns the suspension off on the road to make your life easier. Look for Shimano gears, and Avid or Shimano rim brakes (like you have at the moment) or disc brakes that stop on a disc at the middle of the wheel. Try and go for major brands such as Specialized, Trek and Giant as they offer the best value. Don't go to a chain shop where they will try and sell what's on the floor, not what you need.
Around that price point these are good options-
Trek 4500- http://www.trekbikes.com/uk/en/bikes/mountain_hardtail/4_series/4500e/
Giant XTC4- http://www.giant-bicycles.com/en-GB/bikes/mountain/2442/32687/
Specialized Rockhopper- http://www.specialized.com/gb/en/bc/SBCBkModel.jsp?spid=40637&eid=107
Kona Blast- http://www.konaworld.com/09_blast_uk.cfm
Or my personal favourite-
Norco Storm- http://www.norco.com/bikes/mountain/cross-country-ht/storm/
Don't buy off the internet either- you'll have to get a shop to build it, and if you have any problems you won't have any local support to help you out. At your price point, and your level of riding, full suss is an extra complication you don't need. A hardtail will be lighter. Disc brakes are a real bonus- they make life a lot easier as they're more powerful and cheaper in the long run as pads last longer and maintenance is less. Gears- look for Shimano Deore, or maybe Alivio. SLX is better still. 8 or 9 speed isn't important for the minute- you won't notice enough difference for one to be an advantage over the other..
Hope you enjoy it!