Grey hue on my black and white photos

I have a Sony RX100 and usually (but not always) when I turn a photo to monochrome, it looks like there is a gray layer on top of the photo which I don't know how to prevent or remove. In other words white in the photo is not really white but gray.

See the attached photo for example. I use the software GIMP for editing photos. Using the automatic white balance fix doesn't help. Modifying the "curves" helps a bit but it's tricky. Do you have any advice on how to prevent this or remove it in post production?

A camera usually prevents capturing "burned out" (i.e. all white without any details) highlights. For that reason everything else looks a bit too grey or dark. GIMP made it on my computer is surely capable software but I am admittedly too dumb to use it and or spoiled by other software.

Your attached picture did not show up. Looking through my own ones an all grey one displays a histogram in the curves menu that ends before reaching image white. All I need to do is grab the curve on top and drag it to the left above my whitest pixels. in a next step grab it on the bottom and drag it to the right below your darkest pixels. AFAIK Adobe's overpriced stuff has 3 freely movable triangles below the histogram for black medium grey and white, that make this step more convenient to handle.

If you want to stick with free software from the Linux realm: Give RAW therapee and Darktable a go! Both are by now available for Windows too and quite decent tools for the job.

FTR: "white balance" should get you nowhere. - it is a menu where you decide if a picture should look more amber / reddish or blueish.

I haven't come across any software that handles B&W images gracefully in full auto mode. - Picasa's "I'm feeling lucky" button did amazing jobs on color pictures only. So whatever you'll end using you have to adjust your black and white points manually.

In doubt: Shoot RAW, watch your histogram and maybe adjust your exposure to burn out really surplus highlights on purpose, if situations permit. Great looking B&W images will require a little tweaking in post processing but it doesn't take long.