The train runs west from London Paddington the way to St. Ives at the end of the peninsula. It does not run along the coast, but you can get a bus or taxi from the various stations to your destination on the coast. We have visited Port Isaac and the Jurassic Coast that way ( using taxis).
For the Lake District, if you want to do some nice hiking, consider spending some of your time with HF Holidays, a member-owned cooperative that focuses on guided walking. Non-members are welcome. They have two manor houses in the Lake District, one in the north near Keswick (where we have been) and one more to the south at Coniston. They offer 3-night, 4-night, and 7-night programs at each location, with a choice of 3 guided walks at different levels ( easy, moderate, and more strenuous) each day. The price is all-inclusive: lodging, all meals, guided walks, and transport to the trailheads and back. The accommodations are very nice, the food is varied and high quality (and flexible to accommodate gluten-free and vegetarian diets), and the hikes on offer are well-planned, and include some history and commentary by the guides. .And we really enjoy the camaraderie of the other guests, most of whom are British, with a sprinkling of Aussies, Canadians, and occasionally a French or German person.
Here is an example of the 3-night program and facilities of the house at Keswick:
https://www.hfholidays.co.uk/holidays-and-tours/3-night-northern-lake-district-guided-walking-holiday?format=pdf&vid=1396
The house, as you can see in the photo, is right on the lake (Derwentwater), with a lawn sloping down to the water. It is about a kilometer outside the town of Keswick. They provide directions for using public transport to arrive: train to Penrith and then a shared taxi/transfer from the station right to the house.
It is all very well done. You could spend 3-or 4 nights each at each of the two Lake District locations, or a week at one or the other. The price appears high, but if you add up the lodging, meals, guided walking and transport, we feel it is well worth it for the convenience and reliability.