Heathrow to St Bees train? drive? fly and train?

Look closely at the departure and arrival times of the train routes. The ones that take a ridiculously long time (like 11 hours) are leaving in the evening and arriving the next morning. That's usually because you arrive in Carlisle (or some other connecting station) after the last connecting train has left for the evening, and you have to catch the first train the next morning. I wouldn't want to do that either, especially after a long flight. The good news is that there are plenty of trains during daytime hours that you can take.

If you decide to take the train, then when it comes time to buy tickets (which you can't do yet for September, because tickets go on sale 3 months in advance), then try searching for trains from London (not Heathrow) to St. Bees. That should turn up some cheaper advance-purchase fares that aren't showing up when you search for Heathrow to St. Bees. Then you can make your own way from Heathrow to London Euston, the departure station for trains going northwest. (If you buy an advance-purchase fare, you're locked into taking that specific train, though, so you need to make sure you allow plenty of time in case your flight is delayed or it takes longer to get out of the airport than you think.)

We did the walk about 10 years ago using Contours Walking Holiday. Contour's how to get there instructions are pretty much what we did:

By Rail –There is a railway station at the start of the trail (St
Bees) that is within walking distance of all accommodations. The
nearest railway stations to Robin Hood’s Bay are Whitby and
Scarborough.

For London – There is a train from London Euston to St Bees via
Carlisle or with a change at Preston and Lancaster. The journeys take
between 5-5.5 hours.

We started by flying to Heathrow but spending several days in London before taking the train to St. Bees. My recollection is train from London to Carlisle, connecting to the local train to St. Bees. We returned by local bus from to Whitby then a train back to London. Contours helped us with specific routing advice.

Contours' advice for the West Section walk ending at Kirkby Stephens:
https://www.contours.co.uk/walking-holidays/fact-file.php?id=35

Detailed travel information is sent to you on booking, but we have
provided a summary below.

By Air – The most convenient major city and international airport is
Manchester Airport and Glasgow International. You can then continue to
St Bees by train.

By Rail –There is a railway station at the start of the trail (St
Bees) that is within walking distance of all accommodations. There is
a railway station in Kirkby Stephen that is situated just outside of
the town. No Trains run through St Bees on a Sunday.

For London – There is a train from London Euston to St Bees via
Carlisle or with a change at Preston and Lancaster.

Return to Start – The easiest way to return to the start of the trail
(St Bees) is by taking a train from Kirkby Stephen to St Bees changing
at Carlisle.

It is very easy to travel to the start (and return home from the end)
of the holiday using public transport. Please click here for more
information.

Thank you for the replies. They are very helpful. I am looking in to flying up to Manchester, then taking the train from there. Thanks, especially for explaining the whole "11 hours" travel time. It made no sense to me, but now it does. My flight arrives in Heathrow at 13:20 so I should have time to catch a daytime train. It looks like I have to wait a few months to make the reservations at any rate.

Is anyone still out there? I have other questions.

We have decided to take the train from London to Lancaster, spend the night in Lancaster (close to the train station - any suggestions?) The next day we will take the Northern Line Train from Lancaster to St. Bees (southern route)

1. Is 3 hours enough time (assuming our plane lands on time at 13:20) to get through customs, collect bags and get to Euston Station for a 16:46 train?

2. What's least complicated route from Heathrow to Euston Station?

3. After our hike we will take the train from Kirky Stephen to ??? and rent a car in order to site-see for the next 3 days before returning the car in Edinburgh and joining our tour. Any suggestions of things to do between Kirkby Stephen and Edinburgh. I see Hadrian's wall but have no other ideas.

We're all different, but my preference/practice is to spend a night or two at my destination city (e.g. London in your case) for a number of reasons. First, I like to have an easy, unscheduled day of walking around town to recover from the overnight journey. Second, having a throw away day in my schedule allows for flight delays or problems when I have locked in booking for something like an inn-to-inn walking holiday. Third, I check baggage with my trekking poles and the extra day allows for baggage to catch up with me if it missed a connection. Fourth, it take me time to adjust to time zone/jet lag before a mental/physical activity such as the Coast to Coast.

But if you want to go from air to train:
See: https://tfl.gov.uk/
Heathrow Terminals 1-3 to Euston

Fastest transit route:
Heathrow Express to London Paddington Rail Station
Walk to Paddington (H&C Line)
Circle line to Euston Square Underground Station

Tube:
Piccadilly line to Green Park Underground Station
Victoria line to Warren Street Underground Station
Walk to Euston Square

or

Piccadilly line to Hammersmith (Dist&Picc Line) Underground Station
Walk to Hammersmith (Ham & City Line)
Circle line or Hammersmith & City line to Euston Square Underground Station

The rail service from Lancaster is run by Northern Rail...the northern line is in London
Not exciting but I have stayed at the Travelodge in Lancaster and it's a short walk to The Borough , worth a look for food.
You could take train to Langwathby ,then get a short taxi ride to Penrith where cars can be hired.
There's also a bus service to Kendal

Either way do take the Hartside Pass road on your trip

Kielder Observatory do excellent events.
Some something different ,wildnorthumbrian have shepherds huts and yurts and the nearby pub is perfect.
There's a quirky cafe in a railway carraige in Bellingham

I wouldn't use Warren Street for Euston Station nor would I change at Green Park.

If I were on the Victoria Line I would get off at Euston which is directly below Euston Station.

If I were on the Piccadilly Line I would change at Kings Cross St Pancras and go one stop outbound on the Northern Line or one stop inbound on the Victoria Line to Euston.