Waterproof walking shoes, size 9

[BestIsWest]

Neither style nor beauty but I couldn't find another suitable topic. I am in need of some sturdy waterproof walking shoes, eg North Face Hedgehogs in size 9. I've got some Nike and Skechers trainers for city and path walking but now we have a new pup, I need something that I can trek through muddy and rough terrain with. I balk slightly at paying £120 for the North Face ones but finding it hard to find something similar in a 9 that is reasonably priced.
Can anyone help ( or direct me to the right topic ).

I have long but narrow feet so men's shoes not an option. Ta.

I have these, Salomon Speedcross 3 GTX. They are amazing. I bought them for trail running but I wear them for dog walking now. They are Gore-tex so my feet stay dry, they are really comfortable and they don't slip in even really deep mud. At the end of the walk the mud just rinses off.

www.salomon.com/uk/product/speedcross-3-gtx-w.html

You can buy gaitors to fit on them too. I paid less than half the price on the Salomon website.

Thank you, will have a look at them. How tough are the soles? I think I neespd something flexible but strong for the pebbly beaches round here.