I had my hair bleached blonde in July, then in August I put pink over it (live xxl, semi permanent 6-8 washes).
After it slowly fading I'm left with a horrible pinky grey colour, if I use a supermarket strip kit will it take the blonde out too?

Bleached hair stays bleached until it either grows out or is colored.
But don't be surprised if a product you pick up at the supermarket still leaves you with the pink/gray tones. I would consult a professional stylist about stripping it so that you don't damage it further.

I agree with Lady Sam. Bleach doesn't strip out or wash out, it has to grow out or be covered with a new color.

If you strip this on your own you may end up damaging your hair, or ending up with an even worse problem than you have now. This is not something I'd recommend you try at home, you need a professional.

Next time you want a highlight, try a clip on. It's semi permanent, it's attached to your actual hair, you leave it in, you can wash, blow dry, and style your hair with it in. It's cheaper than paying for color (my daughter had two pink ones put in, $5 each). When your hair grows out a bit you just use pliers, squeeze the attachment, move the highlight up, and squeeze it back in. You will eventually have to replace it, as it's cut to your hair length and moving it up will make it shorten, but it can last for months. The best part, when you no longer want it, you can simply take it out. Also, the color doesn't fade.