You’re using 2 images here.
The “small” version: http://www.mallardsoftavistock.co.uk/images/Tavi_map_small.gif
The large version: http://www.mallardsoftavistock.co.uk/images/Tavi_map_big.gif
The small version is already blurry by itself, and you also resize it using CSS from its original size (900×489) to 880×491. DOUBLE BLURRYYYYYYY ATTACK!!
Here’s what I would do.
Take the large version and open it in your image editor. Make sure it’s in RGB mode, not in “indexed color” mode (that limits the number of colors). Resize (and crop, if necessary) to 880 to 491, or whatever exact size you want to show it on your site. It should end up a little “smoother” than what you have now.
Save the result, and use that version as the “small” version.