Ah, the reinstatement of Sturt Lane Junction! A quick look at Google Earth suggests the land required to achieve this has not been built upon, but sadly I suspect it will never happen.
It would only be the west facing chord of the Sturt Lane Junction on the North side of the SWML. There would then be a new chord on the south side which would allow trains from Frimley to loop, from just under the bridge, around and up to the westbound SWML (probably over party of the lake there).
Any services on the SWML could run in the shadow paths of Woking, Alton or Portsmouth services. As I said it would allow a better connection to trains to, and towards, Waterloo from Frimley and Camberley (by changing at Farnborough, where the are lifts between the platforms). It would also provide connections between stations on the SWML and the Camberley line with a single change at Farnborough or Basingstoke rather than at Woking and Guildford or Basingstoke and Reading (which no one would do because of the time penalties in doing so).
There would also be opportunities to build new stations on each line without showing down existing services (Fleet West, Southwood, Frimley Green and Watchmoor Park to name a few where there could be significant new passengers added to the railway.
Yes it would probably cost several 10's of millions of pounds to build, but it's in an area where there's significant rail usage and the buses are mostly quite expensive (it's often cheaper to go by train between two towns than use the buses), there's significant amounts of traffic and there's likely to only be more going forwards.
Taking the example of Watchmoor Park, this would serve an area which has some houses, but the main use would be to get to the business park there. There's significant numbers of people who travel by bus and train to Blackwater who then walk (until recently without the aid of a footway alongside a duel carriageway) to there.
Likewise Southwood is an area where there's been a lot of houses built and a business park, it had a fairly poor bus service and by providing a train service would significantly reduce parking demand at Farnborough Main.
The new service would connect between towns and villages with over 250,000 residents between them (and most of those would be within walking or cycle distance of the stations) in little under an hour. In terms of extra maintenance costs there would be a marginal increase in the frequency of services on the track which would make up over 95% of the route, which would likely have not much cost implications, even if the service ran twice an hour. Whilst there would be a more significant cost implication due to the maintenance of the new chords they would be relatively short and so the extra costs wouldn't be much more.
If you assume that Farnborough Main is the hub and by providing this service that the total extra passengers were 10% of its current usage (you would get a similar answer if you added up all the station usages asking the lines other than Ascot, Basingstoke and Farnborough Main and assumed they all increased passenger numbers by 10% when they would be seeing a 30-50% increase in numbers of services for an hourly service, which would attract more people traveling between the existing stations) and they all (for the length that they are on the new service for) added £4 of income to the network that would be £1,200,000 (which wouldn't include the extra income from those using the service when they were using other services, which could also be significant). Assuming £400,000 in lease costs for a 4 coach unit, double it given that you'd need two for the service (£800,000) and then add a further £400,000 in other costs (normally lease costs are circa 50% of a TOC's costs but most of these other costs, such as station costs and back office costs wouldn't be being changed, which is why I've assumed 1/3 costs for this) and by this very crude method is likely that the service could cover its costs.
If someone were to do a proper study I wouldn't be surprised if it was significantly better than this.