Most knife sharpening kits that you can buy can damage or scratch your knife. The professionals always recommend using a set of sharpening stones, such as whetstones, or Waterstones. However, these stones often run £40+ and even more for a good sized one. These stones also have the problem of developing a "bowl" shape after repeated use, which in turn requires you to buy another stone - a flattening stone. As you can guess, buying this variety of stones becomes extremely expensive.
A container of Acetone - £10?
Spray Adhesive - £10
A variety of high grit sandpaper - £3/(pack of 5 sheets) * 5 packs = £15
cotton cloths (or cut up an old t-shirt) - Free
rubber bumpers (optional) - £3
smooth bathroom tiles - £0.80/tile *5 = £4
So I used this sharpening kit to sharpen my kitchen knife set, and learned somethings doing so. If you don't know how to sharpen a knife using a sharpening stone/whetstone, etc watch some YouTube videos on how to do so. When you are sharpening using this kit, you only want to PULL the knife back as you sharpen it - as in don't push the knife, sharp edge first, forward to sharpen it. This will prevent damage to the sandpaper, and extend its life.
Use water or windolene as a lubricant. Sharpening stones often required you to use oil or soapy material, sometimes water. Since the sandpaper is a wet or dry type, just use water - that's what it was made for.