This is why Cumbria and Lancaster are so high in the table of counties because lots of people went to Windermere the weekend before lockdown.
It isn't that simple - Cumbria has areas of really high infection, with Barrow being the highest infection rate in the country. A place that have very low tourism levels. What it does have is a shipyard that has remained operational through out this. The security measures on site require all 1500 employees to pass through 4 push through turnstiles as they clock on and off. This means that they get touched 750 times each and every day.... If the person at the head of the queue is infected they have the potential to infect 749 colleagues simply because they had to go through the turnstile
The other hot spots are South Lakeland and this may have been caused by tourists, but it also an area where people commute to Lancaster, Preston and Manchester to work - usually by train which are difficult to socially distance on ( I use it regularly) and travelling through major hub stations. It would be interesting to see how infection rates responded to people starting to wfh / furloughed.
Carlisle - again not a traditional tourist place. Certainly not for walkers.
For the walkers / exercise tourist spreading the infection theory to work you would have to see a big spike in Allerdale around the northern honeypots (Keswick, Coniston etc) - but their infection rates are broadly similar to other predominantly rural areas and lower than urban areas.
I live in a walking / cycling area where we had a really high infection rate, car visitors shot up and remain high because we are an easy drive / good distance cycle from both Manchester & Sheffield. However the infection rate has plummeted because we aren't travelling into work by train because Northern started a Sunday service and less. We simply could not use it to get into town to get to work and do a full day's work and get home again.
Yes visitors have the potential to drive infection rates but there are other transmission vectors that are more common, even in "walking areas". eg local people travelling to a nearby "large" supermarket or simply going to work and bringing it back to their local community.
We are lucky and have a number of people who work in virus transmission and live in the village so have credible community members who have been able to drive home the message that you must act like you are infectious. Not so much someone will infect you (they will) but you have the potential to infect everyone else even if you feel fine and never catch it - you may have touched something and then touched something else.