Although I can't see it happening, I think a service from Carlisle to Perth would be interesting, also stopping at Lockerbie, Carstairs, Motherwell, Whifflet, Cumbernauld and Stirling.
Maybe one like that and also a slow one for intermediate stops swell calling at Carlisle, Lockerbie, Carstairs, Carluke, Shieldmuir, Motherwell, Whifflet, Coatbridge Central, Greenfaulds, Cumbernauld, Larbert, Stirling, Bridge of Allen, Dunblane, Gleneagles and Perth.
Also the fast one could go on to Dundee.
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Lincoln needs more direct trains to London as so far it only has an 07:20 and an 07:04 to London the 07:20 going to Kings Cross and the 07:04 going to St Pancras.
I think there should be an hourly Lincoln-London and an hourly London-Lincoln.
It could go alternate hours so every 2 hours it goes from Kings Cross and every 2 hours it goes from St Pancras International.
The one from London St Pancras could call at London St Pancras, Bedford, Wellingborough, Kettering, Market Harborough, Leicester, East Midlands Parkway, Nottingham, Newark Castle (for Newark North Gate) and Lincoln. The one from London Kings Cross could call at London Kings Cross, Peterborough, Spalding, Sleaford and Lincoln. On saturdays and Sundays the Service from Pancras could carry on to Cleethorpes and the service from Kings Cross could go on to Scarborough.