I have discovered that for me, at least, eating too much fat on a low carb diet, still makes me gain weight. This seems to contradict the information given by Dr Atkins and by Zoe Harcombe, that if you keep insulin levels low by eating no sugar or starchy foods, it is impossible to gain fat. Zoe Harcombe states that the only way fat can be stored is with the help of insulin.
I was curious to understand how I could have gained weight, so I did some more research. It turns out that there is a substance called Acylation Stimulating Protein (ASP), which occurs alongside insulin. ASP can actually cause fat to be stored without the aid of insulin (proved in vitro) but it may call on insulin in the normal course of events. Of course there is always some insulin present in our systems unless we are diabetic. ASP levels rise when high levels of fat are eaten, and in people who have been overweight ASP levels are raised permanently. This could go some way to explaining how people with a weight problem are stuck with it for life.
This is a link to part of the research: http://www.ncbi.nlm.nih.gov/pubmed/1885258?ordinalpos=16&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum
Thanks to Martin Levac and KJF on the low carbers forum http://forum.lowcarber.org/ for pointing me in the right direction