Lakes district - where to base if without a car?

Not much at all Oxenholme.

For me London - York,
York-Penrith ( connecting bus to Keswick)
Good public transport in the north Lakes ,opens up some of the most outstanding scenery in the UK

You could do a lot worse than incorprate the Settle and Carlisle railway in too

There is nowhere really to stay at Oxenholme, at least not without a car. It is a junction station for the Windermere Branch. Kendal is a mile or so down the hill (1st stop on the Windermere train), a big town. Plenty of places to stay there, and only 8 miles on a very good bus service into the Lakes. All the bus routes into the Central Lakes operate out of Kendal Depot, including the Open Top Buses. If coming from York to the lakes you either take a train to Newcastle, change for Carlisle, change again for Penrith or Oxenholme.
Or the hugely more scenic route is the Settle and Carlisle- York to Leeds, Leeds to Carlisle, Carlisle to Penrith or Oxenholme.
I don't think it makes much difference which order you do them in. Either way you are in essence going round 3 sides of a square to transit between York and the Lake District.
You can also do York to Preston (hourly through train which goes on to Blackpool), then Preston to Oxenholme or Penrith. In time terms all are much the same. That is an L shaped journey, passing through quite attractive Pennine scenery then the Lancashire mill towns.
You do Oxenholme to stay in Kendal or Windermere, Penrith to stay in Keswick.

Thanks - i will def encourage them to look into the Settle- Carlisle train as well -

I'm thinking maybe they need to look into staying in Keswick and then branch out around the Lakes from there - if so, sounds like Penrith is the way to go if the times work
T/Y all !

This might work too
https://www.nationalrail.co.uk/times_fares/pr569e360a04000400e942d9601c4cf1.aspx

There are other area passes in the National Rail site,under "Specials"