1968 timetable: (but it looks the same as 1967)
1658 Reading/Guildford - Staines, Egham, Virginia Water, Longcross, Sunningdale, Ascot, all stations to Reading
1700 Weybridge/Windsor - Richmond, Twickenham, Whitton, Feltham, Ashford, Staines
1702 Teddington - all stations except Queens Road then onwards to Waterloo
1709 Hounslow (Twickenham) - all stations
1713 Reading/Camberley - Staines, Egham, Virginia Water, Sunningdale, Ascot, all stations to Reading
1715 Weybridge/Windsor - Richmond, Twickenham, Whitton, Feltham, then all stations
1720 Hounslow (Brentford) - all stations
1723 Shepperton - Richmond, then all stations
1726 Teddington - Clapham, Putney, Barnes, Mortlake, Richmond, then all stations
1728 Reading/Guildford - Staines, Egham, Virginia Water, Longcross, Sunningdale, Ascot, all stations to Reading
1730 Weybridge/Windsor - Richmond, Twickenham, Whitton, Feltham, Ashford, Staines, then all stations
1732 Teddington - all stations except Queens Road (to Kingston)
1739 Hounslow (Twickenham) - all stations
1743 Reading/Camberley - Staines, Egham, Virginia Water, Sunningdale, Ascot, then all stations to Reading
1745 Weybridge - Richmond, Twickenham, Whitton, Feltham, Ashford, Staines, then all stations
1748 Windsor (Brentford) - Hounslow, Feltham, Ashford, Staines, then all stations
1750 Hounslow (Brentford) - all stations
1753 Shepperton - Richmond, St. Margarets, Twickenham, then all stations
1756 Teddington - Clapham, Putney, Barnes, Mortlake, Richmond, then all stations
1758 Reading/Guildford - Staines, Egham, Virginia Water, Sunningdale, Ascot, then all stations to Reading
I have the working timetable for 1968.
Four trains non-stop to Staines (the Reading services) (five listed above, four in the hour 1658-1757)
Six trains non-stop to Richmond
One train non-stop to Hounslow
With two exceptions (1726 & 1756) Clapham Junction was part of the “all stations” stopping pattern, which differs radically from today.
I think the problem is that it's impossible to reconcile the needs of a fast service to Bracknell coupled with the vastly increased need to stop at stations closer to London - non-stop to Richmond or even Staines won't cut it today. 55 years ago places like Clapham were a wilderness with relatively little reason to stop. I lived in the area in the early 1980s and it hadn't changed much then either. Now not just Clapham but Vauxhall are pretty important stops, and then Putney and Barnes also, so you've got four stops before Richmond pretty much all the time. Twickenham and Feltham aren't unimportant either. There's not the track capacity to do both - so today we have plenty of trains but they stop a lot.