The main un-electrified parts of Cross-Country routes are top of the priority list for Electrification (maybe CP6?), I wonder if one reason for them not being given the go-ahead in CP5 was the rolling stock issue?
I.E Plan to convert Voyagers to Bi-Mode with an extra Pantograph, seemingly has too many technical problems to overcome.
If this proves to be the case (too difficult)then you would require new electric stock (Bi-Mode to serve extremities) (expensive) and not many suitable places to cascade overpowered 125mph long distance stock.
Can't see the logic of a rail service between LGW & LHR via Reading - Coaches are faster and more direct via M23/M25 even if the 'western rail link' is built at LHR, it's @ 85 mins LGW - Reading via North Downs line now.
The North Downs line is probably the only compelling case for extending 3rd rail electrification in the UK, Uckfield, Salisbury/Exeter could be 25Kv AC, with dual voltage stock.
Maybe one day!
Current fastest train Reading to Gatwick is:
09:34Reading Station
09:43Wokingham
09:51Blackwater
09:57North Camp
10:10Guildford Station
10:26Dorking Deepdene
10:34Reigate
10:41Redhill
10:50Gatwick Airport
Which is 76 minutes, however if it was run by an EMU rather than a DMU it would have a faster journey time. It should be feasible to run a train between the two airports in about 90 minutes compared with 65 minutes for the coaches.
However the trains maybe able to undercut the coaches as the cost of a return fare for tomorrow (so basicly turn up and go) is £41, however from Maidenhead to Gatwick (via Reading) is £29 for an any time return. Also there is the option (if you travel enough by train in the South East to justify the cost of it) that it is possible for everyone to get a rail card to reduce the cost further.
Also (even if the train fares where comparable) there would be people that would rather travel by train than coach anyway, as you can have access to your luggage, the facilities are nicer, you can walk about, you are not going to get stuck on the M25 in the rush hour, it's greener, the stations are more sheltered than the coach drop off/pick up,
The other thing is that although there may not be lots and lots of people travelling between the two airports there will be a lot of people from the catchment area from the above stations which would like to go to Heathrow, which would make such a service a viable option. As the train doesn't have to travel very far from Gatwick before it becomes quicker than getting to Gatwick before getting the coach to Heathrow.
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Also with a direct train from Guildford to Heathrow it would be possible to get there from the likes of Portsmouth with just one change.
Also with group save 3 or 4 people could travel between Heathrow & Gatwick for about £60 to.