It depends on how you measure progress. It’s quite difficult to squeeze much more out of Southern infrastructure. The gains from electrification and multi aspect signalling were absorbed decades ago.
Resignalling, including but not limited to work to change over to colour light usage and track circuit block principles, actually resulted in a reduction in capacity in some areas. This is not due to the limitations of the newer technology - far from it - but due to the rationalisation which happened at the same time. There are ground frames where there used to be full-time signal boxes, greater spacings for signal sections, fewer crossovers for contingency use, fewer "cripple sidings" for failed trains, single-line sections, etc.
Third rail limits speed gains anyway, as does the sheer density of services on much of the network.
Third rail tends to limit capacity as well as speed gains. There's little point increasing some permissible speeds due to stopping patterns and the need for all trains to stop
somewhere, usually multiple times, on each mainline. This is also one reason why a high-speed replacement of one of the mainlines in the "South Central" area wouldn't really work - there are simply too many places en-route where stops need to be made and capacity needs to be increased.
Sadly, the Southern network in particular has long suffered from terrible arbitrary chopping and changing resulting in an almost total lack of comprehensive clock-face timetables in the peak hours, combined with little service recovery time before the train service is expected to level-out to a clock-face off-peak timetable. This means service recovery is extremely difficult, especially at the shoulder peaks, where the trains may not be the busiest, yet the service still falls apart for thousands of passengers every day. This in turn means bad publicity from passengers who have road-based alternatives (at such times of day), and in turn, the railway fails to attract additional custom from people feeling able to travel for leisure or business outside of the routine high-peak demand.
The station closures that allowed long distance services to be sped up elsewhere didn’t really occur in the more densely populated and commuter oriented South.
Such station closures would have failed due to the sheer volume of demand or due to political pressure. The area is not blessed with a huge number lightly-used stations which can just be closed... and where stations are lightly used, they tend to not impact performance or else have specific spikes in traffic which makes it unpalatable to close them. For example, a train might make up two minutes not calling at Hever, but the revenue from summertime tourist traffic will more than make up for the marginal impact that a station closure (of a facility with minimal upkeep costs) would have.
Dorking to Horsham passes through a largely rural area and the towns at both ends are well served already (think how East Grinstead or Uckfield to Lewes suffered closure under similar conditions), and the signalling reflects its traffic. All of this combines to prevent more trains being routed that way.
The signalling on the Dorking to Horsham route is restrictive, but secondary in impact to the third rail equipment and quality of the permanent way. You can signal 2 stopping services and 1 non-stop service per hour in each direction, and this generally works reasonably well on occasions when it is done, including the odd bit of the peak hours and occasionally to move stock after engineering works. However, that much strain on the track itself would probably need extensive renewals far sooner. The route is an important link between towns in the Chichester area and South London, not to mention Horsham and South London as well. As I've previously posted, I reckon the route could be developed in a cross-London link for Sussex to the WCML if merged with the semi-fast Southern WLL services, but in the mean time, more could be done to improve local connections with a more frequent service, better advertising of the local area, and better infrastructure quality. You only have to look at how relatively well-used the peak time services on this route are; I was shocked when I first went on some of the northbound morning peak services, as they can be very busy indeed by Dorking and Leatherhead. And even despite the small populations of the villages en route, there must also be hundreds of regulars just been Dorking and Horsham via Holmwood, Ockley and Warnham, when combined throughout the day. The larger towns in the area are certainly employment centres on their own.
More generally this terminating at Fareham business happens way too often.
Someone else suggested the turnaround times are too short - with such a long journey, should you be really trying to turn something round in 10 minutes?
Might also illustrate the counter-arguments of trying to run an overly-frequent off-peak service (which has been the philosophy in recent years, so much so that on many lines there is no difference between off-peak and peak frequency) - if there were more spare paths then presumably there wouldn't be such an issue with the return journey running late?
Perhaps, with more Southern, GN and SouthEastern services becoming Thameslinks next year (and thus using 700s, presumably releasing a good number of 377s and other Electrostar variants) they could make an incoming Victoria arrival at Southampton form the next Brighton and vice-versa. That way they'd have safer turnaround times of half-an-hour or so; they could use the sidings west of Southampton if platform space was unavailable.
Platform space is indeed an issue; stations like Brighton and Victoria struggle with anything longer than 10-15 minutes at times, let alone half an hour. A 10 minute turnaround is not ideal, sure, but is very much the imposed requirement on the Southern area. There are also trains which have turn around in that time (or less) on routes in the Redhill area, routes via Oxted, etc. London turnarounds may be better from late 2018, but I can't see the South Coast and Sussex area being much better. If anything, late turnarounds from the Core could make things harder.