
I did that walk a few years ago (starts Battersea Bridge and ends Tower Bridge?) and thoroughly enjoyed it. Would I take a dog? No, I wouldn't take mine but for different reasons to your concerns. It's a long day with lots of pavements, crowded in places and of course lots of traffic. A dog would restrict you should you want to browse along the way i.e. we wandered around St. Catherine's dock and toyed with going on HMS Belfast. Why do they want you to take your dog anyway?