If you are keen on a DSLR, I would have a look at
MPB (banner at top of the page) for
second hand kit.
I don't use Nikon kit, only Canon, so can only recommend their kit (the prices in brackets are prices I have just found on MPB).
I would get something like a 400D / 450D (£259) / 500D (£300), a 18-55 (£40 ish), or the better 18-55 IS (£74), and that would do for general shooting.
Depending on how long you are going away for you could rent a lens from Lenses For Hire (another member / advertiser here) they have the Sigma 50-500 for £52 per week, the Canon 100-400 IS L for £70 per week and the Canon 70-300 IS L for £72 per week. These are the normal recommendations for lenses for safari's when money is less of an issue if buying (each lens is around the £1000 mark), or for short durations if renting.
However, there are cheaper alternatives; at the cheap end of the market you can buy the Canon 75-300 USM for about £170 new, or about £120 second hand. This isn't the best lens in the world (it is generally seen to be Canons worst lens), however, I own it and found it fine on film for two years in Botswana (galleries on my Smugmug - travel / Bots 2004/2005 and Bots 2007) and my Dad found it to be fine on his 400D a couple of years ago - here is one of his shots with it:
http://gembobs.smugmug.com/Travel/Bots-2010/Bradfields-Hornbill-Dad/1007392864_UrJAo-X2.jpg (no idea why he was on ISO 1600, that is straight out of camera as he shot in Jpeg) The 55-250 IS sells for a similar price and is a better quality lens, but not as much reach.
To go up in price, Canon has a well respected 70-300 IS (the black barrelled non L lens) for about £300 second hand, Tamron and Sigma may have similar lenses around that price too.
If you do a search on Flikr you should find groups showing shots taken with the specific lenses you are interested in, this will give you an idea of the picture quality to see if it is something you would be happy with. If you go down the Canon route have a look on Photography On the Net as they have a sub-forum dedicated to shots taken with specfic lenses too.
I would also recommend you buy a tripod (do a search on here for specific recommendations) as you will probably want to take some night shots (the skies in Botswana are amazing, so I would imagine the same is true elsewhere in Africa!) and also for any sunset / sunrise shots too.
Also don't forget to factor in memory cards, take plenty so you don't have to delete shots while over there.
I know of a few people who have gone to Africa with a regular compact camera and have been happy with their shots. I also know people who have gone on safari with only a pair of binoculars too, so horses for courses really. On here we are all keen photographers and are pixel peepers (either out and proud or closet pixel peepers

) but at the very least we want the best possible picture quality we can get, and for many, that means only the expensive lenses will do - your needs and desires may vary!
Hope that helps to give you an idea of what you can get for your budget and hope you have a great trip!