Towels!

Tesco, Sainsbury, Morrisons, etc. Any of these would have some towels. If you have quick-dry camping towels, they are also an alternative to bring.

not all branches of those supermarkets will sell towels - big ones will, small ones won't

so the answer to your question is not necessarily - depends where you are in the Lakes

what a lame rental manager or owner!! Do they think people travel everywhere with towels with them!?

For 3 days, I'd probably just take along a couple thin, worn-out ones from home and leave them behind. Then you'll have room in your bag to take home something besides ratty towels! :)

Camping towels! Brilliant-- might be a great thing to have around for summer anyway! (My kids are always going through towels...though getting better about hanging up/reusing since now they help with laundry...)
--Shelbey

If they don't even provide towels, then dish towels (I'd call them tea towels) are quite possibly not provided either. But every local tourist trap will have Lake District pictorial souvenir towels for purchase. However, they may well be made in China and of poor absorbency.

It's quite normal for self catering holiday lettings such has cottages and caravans not to come with linens. They should supply kitchen utensils but not always cloths and tea towels.

If you're in a bigger city first, there's almost always a TK Maxx.

Tesco will certainly sell towels - if you are driving in you can stop at the one in Bowness on Windermere or, if you're coming around the other way, there is a Tesco in Carlisle as well.
There are four or five hiking/camping stores in Keswick that sell camping towels...George Fisher is the biggest one and my favorite! Pop in, enjoy the store (you can have tea up in the rafters) and pick up what you need. Having been to the lakes many times I find it bizarre that your property doesn't come with towels...that's a fairly big management company there and this surprises me. Oh well! You'll enjoy the area, towels or not!