Thank you for your time.
"Dettol" is a product containing just 4.8% of the active compound chloroxylenol. The formulation already includes soap compounds. A commercial product will always contain provisions to exclude them from any liability from some uses. It doesn't mean that you can't do it, just that they don't want to hear from you if it doesn't work. I didn't find anything, nor do I see any concern for degradation over time from any sources. Usually, any chemical is more susceptible to degradation at higher concentrations. With NO problem for long term storage (at 20-25'C) for the original product, any dilution of it will also be stable. IF you leave it in a hotter environment there may be some breakdown of the compound over time.
I would add to Steven's excellent answer: detergents and soap are all classed as "surfactants" - surface active agents. the division between "soap" and detergents is an historical one in that soap is an ancient invention (documented on cuneiform tablets) and "detergents" which were invented beginning in the 1930's. They all work the same way and are chemically structured according to the same pattern - a "head" group that "likes" water and a "tail" group that "dislikes" water. So when they write something on a label that talks about "detergent" assume that soap is included.
That said, as you have probably deduced, when you add the product to laundry you are in fact mixing it with detergent since you are probably using detergent when washing the laundry. However, the developers of the product have done testing to determine that the product will still have its proper activity given the usual concentration of detergent people use in their wash.There are two reasons for label prohibitions for mixing products. As Steven says, it may inactivate or make the product less efficacious than they're promising and they don't want your mixing of the product to lead you to blame them for the failure of the product to perform. The second reason is that mixing products can cause chemical reactions that result in harmful effects, like classic error of mixing bleach and ammonia. Companies also do not want liability for any harm that might result from these mixtures so it's easier to warn you not to mix things unless they give you the directions for mixing.
Last comment: disinfecting action is VERY concentration dependent. Something can be an effective disinfectant at a threshold concentration and significantly less effective at lower ones. When working with a disinfectant product always follow the label instructions for dilution - you can dilute it too far and fail to get the disinfection action you are depending on.