Using ExpertFlyer, I can see from the pattern of days surrounding it that it's likely sold out, because all the classes are 0'd out, but the very next day (Sunday 18 December) coach (Y) is sold out (0) both flights and there's only 2 seats in business (C2) for sale on the day flight and only 1 seat in business (C1) for sale on the nighttime flight.

I did a +/= 3 day search for LHR to CAI on ES around the date you mentioned) there's different patterns, and it's while it's not quite as sold out around the weekend as it is during the weekend, there's not necessarily many seats available, especially if you care about which cabin you sit in:

The Wednesday before it's C9 Y9 for the daytime flight, and C3 Y9 on the nighttime flight.

The Thursday before it's C9 Y2 for the daytime flight, but already down to C2 Y0 for the nighttime flight.

The Friday before it's C6 Y0 for the daytime flight, but C4 Y0 for the nighttime flight.

However, the Monday and Tuesday after it's C0 Y9 for the daytime flight, but C9 Y9 for the night flight.

And since there are only two nonstop flights, Expert Flyer is showing connecting flights on ES too, and I can see that Saturday 17 December is more sold out connecting flights than on other dates. But I can also tell than in most cases, it's the first part of the connection (LHR to wherever) that's sold out, not the second part (wherever to CAI). So it's seems to be traffic from LHR that's selling out, not traffic to CAI.

So based on that, I would bet that the LHR to CAI flights are selling out not necessarily because of people going to CAI, but quite possibly people using a CAI connection because their other flights from LHR to wherever they wanted to go were already sold out.