There must be a number of chords, curves and spurs which have been introduced over the last few decades, say for example since Beeching, that are on completely new alignments. There are several in London alone.
On another thread in the last few days and weeks, the Waterloo Curve has been discussed. This was used by Eurostar services to Waterloo and has seen its use and abrupt decline in the last couple of decades. This, however, is not the newest track alignment in Britain or London. The Canal Tunnels from St Pancras Low Level to the ECML are on the cusp of entering revenue service for Thameslink trains.
Do we count light rail and metro-type routes? Much of Tramlink follows old heavy rail routes, but a considerable part, especially to New Addington and via the centre of Croydon, is on new alignments.