Sorry what market does a LHR/LGW rail connection serve?
Guildford - LHR was the BAA Airtrack proposal for improving connectivity whist encouraging modal shift; Guildford - LGW would do the same and both could be effected by a semi-fast though service between LHR -LGW.
This would also cater for any LHR - LGW transfer passengers; at the moment both airports advise HEx to/from Paddington, tube to/from Victoria and GEx to/from LGW.
Such a solution would help effect modal shift from car to electric train, speed up transfer times and be far cheaper than Heathwick.