To Kendal by Train
There is a small railway station at Kendal (on the Windermere line) but if you are looking online for trains to Kendal it can be misleading.
The main station for Kendal is Oxenholme AKA 'Oxenholme the Lake District' (to distinguish it from all the other Oxenholmes) which is on the West Coast mainline and usually staffed so you can book seats in advance, buy tickets, get misleading but usually well meant advice etc
Several 'international' trains between London and Scotland stop here but not all of them so check if yours does before you get to Lancaster so you can change there if necessary because the alternative is a visit to Penrith or even worse Carlisle.
Trains from Oxenholme station to Kendal take 4 minutes, if there isn’t one waiting most people either get a taxi or just walk down the hill.
Train Fares UK
if the station is unmanned your should be able to buy a regular price ticket from the conductor - be careful tho as if there is any chance of you gettinga ticket before you get on the train the ticket prices will go up
we boarded a train for Leeds from Barnsley a few weeks ago and were charged 16+GBP - the conductor said to buy them from the ticket office next time which we did and were charged 11+ GBP - adds up if you " let the train take the strain" regularly - doesn't it
Enjoy your stay in the UK