Any railway stations more than 1 change from London?

Here are a couple of candidates:

• Whitby and other stations on the Esk Valley Line. The only mainline connection to this line is Middlesbrough, which currently has no direct service to London (it is planned to begin in 2021). See comment below.

• Thornton Abbey and other stations on the Barton line. It looks like connections would be through Grimsby Town, which also has no direct London service as far as I can tell.

Incidentally, these are both in England.

Firstly the undisputed ones:

• Clitheroe to Hall i’ th’ Wood (excluding Blackburn)
• Barton branch as previously mentioned
• Baildon

Then there are Merseyrail stations from Cressington to Birkdale/Aughton Park/Fazakerley (excluding Moorfields and Liverpool Central). There are sometimes engineering works meaning that London trains run direct from Liverpool South Parkway.

Next there's the stations reachable from London with 1 change, but not To London

• Kirkby to Pemberton (with an overnight stop), thanks to 1 train a day that runs from Buxton via Manchester Picadilly to Kirkby (additionally Wigan Walgate is only 100m from Wigan North Western)
• Reddish South and Denton are reachable from Stockport (no overnight stop needed)

however all those stations meet your criteria as there is no way to get TO London from them with one change.

Finally stations that don't count:

• The Wrexham Central to Bidston branch doesn't count thanks to 1 train a day from Wrexham General, although an overnight stop is required.
• Blaenau Ffestiniog branch doesn't count as there are a handful of London trains that call at Llandudno Junction
• Ashton-under-Lyne has a service to Leeds, and one from Preston, so doesn't count
• I think all Glasgow services call at either Glasgow Central or Glasgow Queen Street, the latter being served by the Calledonian sleeper, so they don't count, indeed I can't find a single service in Scotland that is more than 1 change from London thanks to the sleeper.
• The Whitby - Great Ayton line has summer services to Darlington as previously mentioned (Nunthorpe to James Cook have regular services to Newcastle)

Living in Liverpool, I can't believe I missed the obvious fact the Merseyrail Northern Line trains don't go through Liverpool Lime Street - they run from Hunts Cross to either Southport or Ormskirk via Liverpool Central (and so you have to do 1 stop on the Wirral Line or walk to Lime Street). No station on this line has a normal service to London. (However, Lime Street is currently undergoing major renovation, and so London trains are terminating at Liverpool South Parkway, meaning that London with 1 connection is possible for 3 weeks only.)

You're asking for stations within the UK.

For any station in Northern Ireland, you'd need to change from train to ferry and from ferry to train. On either side, (direct) trains do not connect all the way to the ferry terminal, so that means more than one change even to reach Belfast, and more than two to reach any other destination in Northern Ireland.

The West Highland Line is famously about as remote as you can get and have a direct train to London, but it qualifies one day a week - there is a night sleeper service to Fort William through Glasgow Queen Street, but it doesn't run on Saturday nights. Queen Street has no other direct connections to London so you'd have to make a short walk to Glasgow Central to change, and I'm guessing this would count as more than a simple change for your question.

More prosaically, trains on the Maryhill Line would also qualify - they only seem to serve Glasgow Queen Street.

I think the stations between Kirkby and Wigan Wallgate don't have one-change services to London.

ie Rainford, Upholland, Orrell and Pemberton.

Their services run between Kirkby and Blackburn, via Wigan Wallgate and Manchester Victoria. There's no direct service from any of those stations to London, you can change at Wigan Wallgate for Wigan North Western or at Manchester Victoria for Manchester Piccadilly.

Stations from Wigan Wallgate to Manchester along that line also have a service to Manchester Airport via Manchester Piccadilly (which originates at Southport) and you can change at Piccadilly for London.

I can't find any other line through Manchester Victoria that doesn't also have trains to Piccadilly, or have access to another station like Wigan North Western, Leeds, Brighouse, Bradford Interchange or Preston.

Eskdale in Cumbria would possibly count here - from London you'd have go up the West Coast Mainline and then change to the Cumbrian Coast Line at either Carnforth or Carlisle then from there go to Ravenglass and change to the Ravenglass & Eskdale Line.

Marlow in Buckinghamshire can only be reached via Bourne End, which can only be reached via Maidenhead - 2 changes from London Paddington.

I suspect this could be the nearest, about 30 miles away and less than 1 hour total journey time from London Paddington.