IF such a junction were to exist (as would the north to east junction of Sturt Lane and/or a nort to west junction to provide a link from Farnborough to Frimely which I have suggested elsewhere) then it would have to be fully grade sperated.
The cost of this for the Sturt Lane Junction (according to Surrey County Council's report) is £75million. However, have you seen how little space there is around the North Down's Line where it passes under the SWML? I don't think that you could fit anything in there.
Also, although it may be possible to run south to west from the Frimley - Aldershot Line to the SWML I do not see that the return link would be possible (leaving aside the fact that the line to south of here is single track which pretty much always has a train on it meaning that it would have to be doubled - note not re-doubled!).
Even if such a link were to exist it wouldn't save much time as to go from Farnborough to Guildford via Woking is about 20 minutes slower than the about 20 minutes that it takes to go direct. Most of this time benefit could be wiped out by those from Basingstoke and south or west if the new service called at the local stations between Basingstoke and Farnborough combined with the likelihood that the trains from the south and west would likely have a connection time of (say) 10 minutes with such a service at Basingstoke or Farnborough.
By the time a 10 minute connection time is allowed for (so that there is time to make the connection even if the service is running 5 minutes late) and a slightly longer journey time of 5 minutes is included then the time difference is down to 5 minutes, which makes it hardly worth doing.
Either way (changing at Woking or using a new service) for most people it would still require a change of trains, unless the new service was to serve the West of England Line and the SWML to Southampton. However, that would use up several paths which would otherwise be used (post Crossrail 2) for more profitable services to London.
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Only if it were a flat Junction, which is not what Surrey are currently proposing. However, the bigger problem is that there are no paths into Waterloo. The only way around this as I see it would be to extend the Woking-Waterloo stoppers, however that wouldn't bring the time savings that Surrey are looking for. It would also require improvements to the junction at Woking sooner. (but that is going of the main course of this thread and have been covered
here)