A good inner tent would have been treated to stop the fabric holding water, so using something like Nikwash Techwash will clean and replace some of the treatment.
Techwash is a liquid soap, so it will clean stuff but there's nothing in there that would replace a light proofing treatment. A big point about Techwash (or other pure soaps, I use Dripak Liquid Soap Flakes as it's much cheaper but pretty much the same!) isn't what it does so much as what it doesn't, in particular leave any traces that will work to reduce surface tension in water droplets so they penetrate the fabric easily (which is how detergents work: great for getting things clean, but...).
However, since tent inner walls generally don't get much abuse the original coating should be there for a long time before you'd need to do anything about renewing it.
andrew_s wrote:What's death to water repellent coating is fabric conditioners. Don't use anything that may have a fabric conditioner in it, and don't use a washing machine that has had fabric conditioner in it recently (last dozen washes or so). This applies to waterproof jackets as well as tent inners.
They are indeed a Work Of Stan, at least as far as technical fabrics go. They don't so much kill coatings as smother them in goop (the difference being if you can get the goop off you might have something worth saving). So as well as Andrew's caution on conditioners on jackets and tents, add to that pretty much anything with technical performance fabrics (base layers, windproofs etc. etc.).
Often seen riding a bike around Dundee...