Lake District and trains or other public transportation

Yes, it is a 3 hour train journey whether you go northabout via Carlisle or southabout via Lancaster/Barrow. This is chiefly due to a few very pesky big mountains in the way.

When you get to Ravenglass it is about a 30 minute walk up the hill (or a limited Summer weekend bus). I highly recommend doing the walk as a circular- out via Walls Roman Bath House (the highest extant Roman standing structure in the UK and the real end of the coastal fortifications relating to Hadrian's Wall) and the lovely woods on the edge of the estate, back via the sidewalk on the road. At this time of year those woods are just beautiful.

From Ravenglass the Romans cut up through Eskdale, over the Hardknott Pass and on to Ambleside.

Before Covid there was a weekend bus from Penrith and Keswick via Ambleside, Coniston and Broughton in Furness, to the castle gates, but I was usually the only person on, so it never restarted.
Especially southabout it is a beautiful ride up the coast.
If you buy a Family Lakes Day Ranger (currently £58.80- two adults and two children) that covers all trains Penrith to Lancaster, via the coast as far north as Workington, all Windermere Lake Cruises and all buses in the County. A corner can be cut by using double deck Bus #6 from Windermere to Barrow in Furness Railway Station approach.
Another way to do the journey on that ticket is bus to Keswick, bus to Workington, train to Ravenglass. Not much shorter in time terms, but a way to make it a wonderful scenic day trip.

I'm fifteen miles up the coast from Ravenglass and do that as a round day trip all the time.

Windermere or Ambleside would do for Beatrix- it makes very little difference- Mountain Goat pick up I believe in Ambleside.

The Manchester to Windermere trains are run by Northern Rail, so use their website, and get one of the through trains from Manchester Airport and Manchester Pic.

Get yourself a family and friends railcard- a third off your rail fares and 60% off the children's fares.

Thank you! 3 hrs train ride seems a bit far though if he ends up keeping his heart set on it, we can pursue it.
Thank you for the rail card etc links!

Is Booking.com as good a place as any to be looking for apartment short term rentals? There are several in Ambleside that look nice, though pricey, though that's probably to be expected both in Ambleside and London. I am ordering Rick Steves' London Guidbook. I do have the Best of England, but hoping for more details to steer me the right way for London. It's all fairly overwhelming to me, but I get overwhelmed at big projects.

As well as booking.com I would try Visit Cumbria, and maybe some of the local lettings companies. The one I am familiar with, as I frequently pass their offices, is Sally's Cottages.

In the Lake District you are more likely to find a cottage than an apartment. Although writing that brings back memories from, oh, over 50 years ago of an apartment we used to have each summer opposite Hayes Nurseries in Ambleside, and another above Threlkeld Post Office.

It'll cost you but might Mountain Goat give you a bespoke tour to Muncaster? They do, or did, a scheduled trip over to Muncaster via Hardknott and Eskdale, so might put a bespoke one together if you ask them.

Thank you! I'll contact Mountain Goat. And a cottage sounds lovely.