I've bought my mother a Scroll 7D 7" tablet for Christmas. I'm currently setting up various things so that it's ready for her to use when she opens it and have been trying to download images from Google of her favourite singer but I just can't figure out how to do it.

I have an iPad mini, my son an iPad 2 and his dad has a samsung. On ours, all we have to do is click on the image and select save to camera roll but on this the only option is to share via email/Facebook/skype etc.

Does anyone know how to do this any other way apart from emailing it and saving it that way (assuming that will work)?

You should be able to long press on the image, and then choose 'Save image'.
That usually downloads to the Downloads folder and adds it to the Gallery.
At least that's what happens on my Motorola Xoom.

No, tried that but nothing happens, unfortunately.

Sometimes you have to try a couple of times before the dialogue comes up, and of course some sites block downloading of images.

Does no dialogue ever come up when you long press?

No, all I get is a row of 3 dots on the top right of the screen. Press that and I get option to share via Gmail, Twitter and FB, no option to save to gallery/camera roll.

Well the three dots are the browser menu.
What I mean is a pop-up dialogue when you press and hold on an image. It is the touch equivalent of a right click, and is fairly much ubiquitous.

It is browser specific, so on the stock browser the image downloads go into the gallery, but if I use the Maxthon browser they don't, but you can still find them in the downloads app.

I'm not familiar with that particular tablet, and my Xoom only has Android 4.0 rather than the 4.2 on your one.
Perhaps someone else has more specific knowledge?