With my fantasy £16 Bn I'd create an M1 rail route, by building a number of infill sections of new and rebuilt track along with a few stations to link the WCML and Midland to create an M1 train service, a reasonably direct rail route connecting all the major cities and towns along the M1 motorway, combining parts of the WCML and Midland into a new route.
Starting at St Pancras using the MML upto Luton, then at the northern end of Luton where the MML runs alongside the M1 a new section of track over to the WCML south of Bletchley, follow the WCML through Milton Keynes upto Northampton then to get to Leicester, either reopen the Northampton to Market Harborough or, take the slow lines upto Crick, then a new line following the A5, under/over the M6, then drop onto the old GCML route along the M1, through Lutterworth with an M1 Parkway station, into Leicester. MML upto Nottingham but take the Erewash valley line.
On the edge of Nottingham, south of Long Eaton I'd rebuild the long demolished 'Trent Station', branding it as 'Derby-Nottingham Interchange' allowing trains a convenient interchange between North-South services and Derby to Nottingham local services. New M1 Parkway at Trowel, MML upto Chesterfield, Sheffield, Barnsley, Wakefield Westgate with a new curve, then onto Leeds.
Possibly a couple more strategically placed M1 Parkway stations.