How do I get stains/limescale off my bathtub? Nothing seems to work.

Scrub free is magical on soap scum. CLR (which smells awful to me) cleans limescale well. When I moved into my new house I had lines in my toilette where the water runs and like a ring around where the water sits, and neither of these cured it, which had never happened to me. I had always been able to get everything to sparkle. One day I hired Merry Maids to clean. and one of the women got most of it out with a pumice stone. I was thrilled.

Sounds like your tub needs to be refinished. There are professionals who do that.
If you are a do-it-yourself type of person;
http://www.ehow.com/how_2080903_refinish-antique-bathtub.html

As @JessicaisinLove said, the porcelain is damaged. Get it reporcelained.

Things like pumice and abrasives do more harm than good. Refinishing it is probably your best bet. But first, I’d try baking soda and food grade (35 percent) hydrogen peroxide. Be careful with it.

As a former hotel inspector, here are 3 things learned about tubs:

1.) Lime build-up: it is the easiest to remove. Vinegar works well. If it is on the shower head, pour some in a plastic bag and secure it to the shower head for soaking. If on a wall, soak some paper towels and secure them over the spot. It may take awhile depending upon the amount of build-up

2.) Stains – something that can be cleaned. Many porcelain tubs have an added non-slip surface that has the potential to stain over time. It can be cleaned easily with certain products like a Magic Eraser (which the UK doesn’t seem to have yet…checked Tesco’s and Argos.)

3.) Discoloration – porcelain tubs are typically metal with a thin coating of porcelain or enamel. Over time, the surface can be worn away from abrasive cleaning products, water pressure, and possibly other reasons. This type of tub can be resurfaced by a professional, but I have yet to see one that looks good and/or holds up.

If it ends up being a discoloration, focus on the fact that the tub is clean. You can adjust the water pressure and clean the drain to prevent it from getting worse. A rubber mat can always be used to hide the blemish, but personally, they gross me out as they are virtually impossible to keep clean. And you always have the option of replacing the tub.

You don’t say what kind of stain it is, but if its a rust or iron stain try Zud, which has oxalic acid in it or pure oxalic acid which you may be able to find at your hardware store, sold as wood bleach. It works like magic on rust and iron stains if that’s what the problem is.

Vinegar works well but on the sides of a tub it’s hard because it needs to soak on the limescale. Try something thick like Limeaway. If you can get it slightly loose you can scrape it off with a putty knife.

This is most likely a place where the water path has worn off the glossy top layer of enamel, exposing a rougher, more porous layer. Dirt will always stick more easily to this and it will never shine like the rest of the tub. The only real solution is refinishing.