Two things to try...
One is an OXY product. I have never used this on carpet, but I have removed dye stains from other surfaces with it.
Get some OXY10 (face cleanser) and rub it into the dye. If possible, put a heat sourse such as a lamp over it. I put the item in the sun, which in your case is not possible. Let it soak in for a couple of hours. If you see a difference, reapply and leave it on longer.
The other thing I have recently discovered that works good on removing stains from carpet, is Greased Lightening.... This is a cleaning product sold in stores here in the US. I don't know how it would work on hair dye, but it did remove a red juice stain for me.
I recently dripped hair dye onto my carpet, and managed to get most of the stain out using perm lotion from a Home Perm Kit.
This advice was given to me by a hair stylist who uses perm lotion to remove stains from her towels and gowns in the salon.
I had the same problem..Burgandy hair dye beige carpet..I put rubbing alcohol on the stain then OxyClean or an oxy cleaner of some form poured more rubbing alcohol over it and scrubbed with a wet rag and it came right up. But I also found the longer you let the mixture sit on the carpet the less you have to scrub!
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