I'm relatively new to illustrator and am sure that what I'm asking has a very simple answer but I can't seem to get my head around it! I want to change the shape of this text to a curved line which follows the edge of the logo:
The text file sent over by my customer is a jpeg and I can't re-create the text as it's a google font. Any advice will be much appreciated.
You're not going to be able to alter the text in a .jpeg image in illustrator, it simply can't be done. Possibly you could do that sort of manipulation in Photoshop, but I'd strongly recommend against it. What I would do is first go back and ask your client if they can provide the font file that was used for the "the old school henstead" line. If they can, you can then mask over the current type in the jpeg and use the Type on a Path option in illustrator to recreate the text so it mimics the curved patch of the top of the shield.
If your client does not have the font file, you're going to have to do some legwork to find an alternative font that matches the one thats in the image. I've had pretty good success using What the Font to help find a close match. You'll then have to purchase the font and proceed with the steps above.
If you need a font replacement I would recommend checking out google fonts for some free fonts. Some fonts in particular you may want to check out there are: Lora, Droid Serif, Vollkorn, Cardo, and Lusitana. They are viable alternatives to the current font. Just download the one you want to replace the current text with and then you can use photoshop to create the curved text.
To make curved text in photoshop you want to create a curved line with the path tool. You can see what I did in the screenshot below. I used the path tool to make a line and then added an anchor in the middle to pull it up and make it curved. Then you switch to the text tool and hover over the line until you see the cursor change. Click the line and you can now type on the line.
I agree with the others that this isn't the best approach as you can see in my screenshot it doesn't look perfect. (For example, the o's aren't lined up right) The best way to do this is to use Illustrator or some other vector-based program.
It's not perfect (I just made it really quick to show you the difference), but I remade your logo in Illustrator. Here's a screenshot below. You can see its much better for this sort of thing. The curved text looks much and this file can be made any size without losing quality.
.jpgin Illustrator--that program is made for creating and editing vector files. You'll want to try your luck with Photoshop, GIMP or a similar raster file editor.