How can I copy a font from an image

Hi, I'm trying to recreate a client logo in illustrator from a provided low res .jpg. I've recreated the design elements using the curvature tool but the font is a problem.

The client doesn't know what font was used originally and I can't find a match anywhere. I can't really use the curvature tool because the font is heavily pixelated when zoomed in. 

I've also tried magic wand and the creation of a work path in photoshop but as I can only set the tolerance to 0.5px it brings in a load of points I don't want. As a result, the import looks crazy when I paste it into my illustrator project?

Any help would be greatly appreciated?

TIA