I ran some estimates for a South Coast Shinkansen, stopping all stations:
| Station | Time (min) | Current time (min) | Advantage |
| Waterloo | 0 | N/A | N/A |
| Clapham Junction | 7 | 8 | 1 |
| Gatwick Airport | 20 | 29 | 9 |
| Brighton | 33 | 58 | 25 |
| Littlehampton | 45 | 105* | 60 |
| Portsmouth and Southsea | 58 | 87* | 29 |
| Southampton Central | 69 | 75 | 6 |
| Bournemouth | 82 | 106 | 24 |
This assumes 60 seconds of dwell at all stations, using exemplar stations on the Tokaido-Sanyo Shinkansen with similar spacings to the spacings here. Top speed is effectively ~285-300km/h as a result.
Clearly the Brighton Main line is the main beneficiary, especially for Brighton. Gatwick is less spectacular but given that this would be ~10tph at this running time, it almost certainly thrashes the Gatwick Express et al. This likely means major service reductions are practical, for example, from the 8tph to each of Thameslink and Victoria to 4tph to Thameslink. Which would be a net saving of 12. Presumably you'd rejigg everything to use up the 4tph but the details of a total recast of services to the south coast is out of scope at this time.
Arun Valley line is probably reduced to a shuttle between Littlehampton and the Airport, and the Coastways take on new importance for moving passengers to the Shinkansen stations. Gatwick Airport and Brighton have 60% of entries/exits on the BML south of East Croydon.
By the time we get to Portsmouth we have a ~30 minute advantage, which is going to kill the Portsmouth indirect service by Eastleigh, and probably cut the overall frequency on the Portsmouth Direct Line by one (for two remaining tph).
So that's now a net saving of 14.
Moving onto Southampton the journey time saving is only 6 minutes, although 10tph vs 3 fast tph means that I would expect virtually everyone to switch regardless. I reckon you could probably cut it to two fast-ish trains per hour to Southampton for a reduction of one. Noone is going to take the SWML for London-Bournemouth because the journey time advantage is crushing again.
So I would make that a net reduction of 15 trains per hour into London. Mostly on theBrighton Main Line but I think significant cuts elsewhere are achievable.
A lot of traffic at the likes of Winchester or Petersfield is likely to end up in a situation where optimum routings will vary wildly based on the time of the hour. If the southbound train is coming soon it will be faster to double back over the Shinkansen, whereas if the northbound train arrives earlier it will be faster to head direct. That rather challenges the simplistic frequency estimate but its really hard to do a better analysis without properly designing a timetable.
15 trains per hour is roughly equivalent to the off-peak service out of the Southern side of Victoria, so scrubbing that much demand is likely to allow major changes in central London.
Would be a very expensive ~210km long line to build, but even using Series 800 Shinkansen seating (2+2 and 1.1m of seat pitch!) would still allow 10+tph of 1100 seats and plenty of standing room. Each seat width and the gangway width could each be ~13.8cm greater than in the Class 800.
