I'm pretty sure that a family in London would not be eating turkey, either, unless they were wildly iconoclastic in their dietary preferences. While some turkeys may have been imported from the Americas by that time and made it to market, the traditional English feast poultry was the goose. Even in Conan Doyle's day they were raised and sold to Londoners for Christmas dinner (ref. "The Blue Carbuncle" for details).
With respect to the suspect almond cheesecake, according to www.cheesecake.com
(who should know, I suppose):
"As the Romans expanded their empire, they brought cheesecake recipes to the Europeans. Great Britain and Eastern Europe began experimenting with ways to put their own unique spin on cheesecake. In each country of Europe, the recipes started taking on different cultural shapes, using ingredients native to each region. In 1545, the first cookbook was printed. It described the cheesecake as a flour-based sweet food. Even Henry VIIIís chef did his part to shape the cheesecake recipe. Apparently, his chef cut up cheese into very small pieces and soaked those pieces in milk for three hours. Then, he strained the mixture and added eggs, butter and sugar."
However, that's irrelevant, as everyone knows the traditional English Christmas was the pudding, usually of the plum (actually, raisin) variety. I suspect the author was describing his/her family's own traditional dinner, or at least one that s/he would like to have, rather than one for the period.