"Old wild west" secret sauce
I've never been to Old Wild West but that looks very much like "fry sauce" or "secret sauce" as we use them here in the United States. In looking at Old Wild West's website, it appears to be geared around offering traditional US style burgers, fries, steaks, ribs, etc. so the inclusion of US style fry sauce would make sense. Here is a link to a typical version that would be used here: http://www.epicurious.com/recipes/food/views/epicurious-not-so-secret-sauce-51261820