There are 2-3 cheaper ways to get from LGW to LHR that I can think of.

Perhaps someone can verify the fares.

Method 1 (simplest):

Buy ticket at LGW for West Brompton.

The OW ticket was GBP 7.50 a year or 2 ago. Train takes about 30-35 minutes.

Buy a zone 2-6 London Underground ticket at West Brompton. Take District Line the one stop to Earls Court. Change for a train to Ealing Broadway or Chiswick (one that gets you to Hammersmith, Barons Court or Acton Town.) Change over to Piccadilly Line train to LHR.

This skirts going into zone 1 which saves a little bit going in and out.

Method 2:

Buy ticket to East Croydon. Buy a Zone 2-6 or 1-6 travelcard if on a weekend/holiday, or after 9:30 M-F. If buying a Zone 2-6 ticket, take a train to West Brompton and continue as above.

Otherwise, take a train to Victoria or Blackfriars. Take London Underground for there to LHR.