Those dogs would love the Lake District mate but when you go fell walking round there,you will be known as a "Crag Rat" to the locals.These Crag Rats used to spoil my days pike fishing in the lakes by not putting their dogs and kids on a lead.Loose dogs would run through dead bait lines and kids trample all over my gear.Nearly got into a couple of fights over it ffs.
You are more than welcome in my county Wile as long as you follow the "country code".haha.
Try a days fishing at Grasmere in the summer you will see what i mean.It can get very busy at certain times of the year,i was surprised how busy it can get.
I would say off peak times would be best for peace and quiet mate,i suppose it depends on which part you go and how much you like walking.
Thought id best warn you pal.