Question: How many miles long is this major railway link between London and Edinburgh, in which The Swinton-Doncaster line is a short railway between Swinton Junction and Doncaster South Yorkshire?

Context paragraphs:
Barnsley Coal Railway: The Barnsley Coal Railway was a short railway which, when fully opened, ran between Stairfoot Junction, on the Mexborough to Barnsley line of the South Yorkshire Railway (SYR) and a triangular junction at Nostell on the line of the West Riding and Grimsby Railway (WR&GR).

East Coast Main Line: The East Coast Main Line (ECML) is a 393 mi major railway link between London and Edinburgh via Peterborough, Doncaster, Wakefield, Leeds, York, Darlington and Newcastle, electrified along the whole route.  Services north of Edinburgh to Aberdeen and Inverness use diesel trains.  The main franchise on the line is operated by Virgin Trains East Coast.

Swinton–Doncaster line: The Swinton–Doncaster line is a short railway line in South Yorkshire between Swinton Junction on the Wakefield Line and Doncaster South Yorkshire Junction on the East Coast Main Line.  The line comprises the former North Midland Railway's "Swinton curve" between Swinton and Mexborough and the east end of the former South Yorkshire Railway Blackburn Valley line, between Mexborough and Doncaster.  Northern operates passenger trains on the line; TransPennine Express and CrossCountry use the line but do not provide stopping service.

Denaby and Conisbrough railway station: Denaby and Conisbrough railway station was a small station, the southern terminus of the South Yorkshire Junction Railway branch from Wrangbrook Junction.  The station, built to serve Denaby Main and Conisbrough, near Doncaster, South Yorkshire, England, was situated just to the north of the Mexborough to Doncaster line of the Manchester, Sheffield and Lincolnshire Railway, close by the road linking the villages in its name.  Access to the station was by a subway under the G.C. line.

Swinton (South Yorkshire) railway station: Swinton railway station is a railway station in Swinton, South Yorkshire, England.  It has three platforms and a small bus station, and lies at the junction of the former North Midland Railway main line between Rotherham Masborough and Leeds via Cudworth and the former South Yorkshire Railway line to Doncaster.

Swinton Central railway station: Swinton, later Swinton Central railway station was situated on the South Yorkshire Railway line from Sheffield Victoria to Doncaster, between Kilnhurst Central and Mexborough.  The station was to serve the community of Swinton Bridge, near Mexborough, South Yorkshire, England.

Doncaster (St. James' Bridge) railway station: Doncaster (St. James' Bridge) railway station was situated in the Hexthorpe area of Doncaster, South Yorkshire, England and was accessed from St. James' Bridge, the main road link between Doncaster town centre and the railway community of Hexthorpe.  The station was a little nearer Doncaster than the South Yorkshire Railway's Doncaster (Cherry Tree Lane) railway station being less than a mile south of the main station, adjacent to the Sheffield line.

Pickburn and Brodsworth railway station: Pickburn and Brodsworth railway station was a small railway station situated on the South Yorkshire Junction Railway's line between Wrangbrook Junction and Denaby and Conisbrough.  It was situated 4.5 mi south of Wrangbrook Junction, just inside what became the South Yorkshire boundary and was intended to serve the hamlet of Pickburn, which was close by, and Brodsworth, near Doncaster, South Yorkshire, a short distance away.

Reading–Basingstoke line: The Reading–Basingstoke line is a short railway link between the South Western Main Line and the Great Western Main Line, constructed by the Great Western Railway between 1846 and 1848.  The line is served by Great Western Railway local services between Reading and Basingstoke, which stop at the intermediate stations Reading West, Mortimer and Bramley.  The line is also an important through route for longer distance passenger and freight services: CrossCountry services from Bournemouth and Southampton to Birmingham and the North of England and freight trains between Southampton Docks and the Midlands use the line.  The section of line between Southcote Junction and Basingstoke was resignalled in 2006, to increase the capacity of the line.

Rother Valley Railway: The Rother Valley Railway (RVR) is a heritage railway project based at Robertsbridge in East Sussex, England.  It takes its name from the original name for what later became the Kent and East Sussex Railway, running from Robertsbridge through to Headcorn in Kent, via Tenterden.  The project is to replace the ‘missing link’ between Robertsbridge, a station on the Tonbridge to Hastings mainline, and Bodiam on the Kent and East Sussex Railway, a heritage railway which operates from Bodiam to Tenterden.  A charity supported by a society of volunteers are attempting to re-establish the railway link.  The RVR began by reinstating the first few hundred yards of line eastwards from Robertsbridge, and also a short stretch westwards from Bodiam.  In 2010, the latter section was further extended to reach Junction Road.  In summer 2011 work began at Robertsbridge to extend further eastwards to Northbridge Street, which entailed the rebuilding of five bridges.  By June 2012, this further extension was also completed.  In September 2013, a Gala weekend at Robertsbridge marked the progress to date and the start of the next phase - the re-instatement of the section between Northbridge Street and Junction Road, for which statutory permissions are being sought.  While the RVR does not yet feature regular passenger trains, the base at Robertsbridge houses a small shop and visitor centre open to the public each Sunday, utilising a building formerly used as the London terminus of the Orient Express.  There is also a small collection of historic railway vehicles in various stages of preservation.

Supporting paragraphs: Swinton–Doncaster line East Coast Main Line
Answer: 393 mi