A Western or Southern rail link to Heathrow is something the airport ought to welcome as it further benefits the surface access mode share, and one or both will almost certainly happen at some stage. But for capacity reasons this will require the HEx paths to continue beyond the airport on something that is more akin to a typical suburban service, and if so the ultra-low-density layout of the HEx would be something of an anomaly when operating a more "normal" rail route with a mix of airport and other passengers. There is also the technical issue that the HEx trains probably aren't convertible to DC supply, which would probably be essential to operate a southern link, so if this is the chosen option the units themselves will be unsuitable.
For these reasons and because if it remains the same HEx will lose some mode share to Crossrail, I would expect to see HEx evolve from today's rather ostentatious offerning into a less differentiated service rather similar to Gatwick Express. But I think while Gatwick Express should remove its premium fare to enourage airport passengers off the Brighton fasts, there is a case for HEx to retain a more modest premium between Heathrow and Paddington to reflect the fact it will genuinely still be the fastest option for many airport passengers. The use of the same trains for other journeys such as Woking to Old Oak for HS2 interchange will offset the likely reduction in Heathrow-Paddington passengers.
Depending on the calling pattern (especially during the peaks) there could be capacity problems on the existing units between Guildford and Woking (so I'd expect that there could be restrictions on that). However on the services to/from Basingstoke (which would, other than those going to Heathrow, be used for local services) would be fine as the numbers of people traveling between the stations between Basingstoke and Woking (regardless of they stop at all the stations or only limited stops) would be fairly limited compared to the capacity of the trains, but a very welcome increase in capacity.
Hook station, with about 800,000 current passengers is likely to see significant growth over the next decade with circa 800 houses with planning permission and over 100 of them currently being built. On top of that there's several flats which are being marketed having been converted from an office building and other developments working through the planning process (including 700 houses which have just been rejected but are likely to be back again, either through a new planning application or planning appeal.
Winchfield could see a new town (upto 2,500 houses) either in close proximity to the station or a short distance (say 20 minute walk).
Fleet is also seeing additional development and Farnborough, although there's no significant developments due, is a major town with a significant number of employers which draws a significant number of people from the surrounding areas.
As such all of those places would likely see significant growth if train frequencies were to increase. As I've suggested elsewhere (as 4tph at Winchfield and Hook could be overkill) one of the current London services could switch to run to Farnham or skip these stations or the Heathrow services could be 1tph to serve Hook whilst the other 1tph to serve Winchfield giving each station 3tph. Any of the options would give 3tph at those minor station (although Hook could have >1 million passengers so isn't that minor in the greater scheme of things) and 6tph for Farnborough (with a mixture of calling patterns, such as 5tph to Woking 3tph to Hook/Winchfield, 2tph to Heathrow, 4tph to Waterloo, which bearing in mind it currently has circa 3 million passengers a year probably isn't too much overkill especially if the extra few services increase passenger numbers).
The problem is that the image of an express service wouldn't work well if it were calling at most stations, however if it didn't call at those stations (so running fast from Basingstoke to Woking it would skip past 4 stations which currently add 6 million passengers to the rail network and where there's plenty of extra passengers who could be added to the network if there were more frieght trains (especially to Heathrow) in either the form of leisure or, potentially more importantly, business travelers who currently (from my experience) mostly use taxies to get to Heathrow.
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