Newcastle Northern Runner. Sports shoes website. Start Fitness. Wildtrak. All do running/Trail runners. New Balance in Keswick but selection less now as most get sent to Sports shoes to be sold at a lower price.
The New Balance shops in Shap and near Maryport usually have a better selection.
New Balance do good trail running shoes in a variety of widths, and different models suit different foot shapes. It's probably easiest to visit one of their outlet shops in Cumbria to find out which one is best for you.
If you do decide to go to the Lake District, some of the valleys leading into the Skiddaw/Blencathra group from the east and north would be good. They are never very crowded, offer plenty of wild camping spots and are pretty easy to navigate, but offer options of hopping to a neighbouring valley or up a fell or two. A bonus is that parking is generally pretty easy to find, safe, and free.