Prices of most commodities rose by 50% over the period of the war, others by much more. Fresh meat would increase by some 100% (imported, frozen meat almost twice this); fish by almost 200%, sugar by 250% and fresh eggs by 400%.
In 1914, Britain (pdf, 2014) was 100% dependent on imports for sugar yet was 50% self-sufficient in fresh eggs. For meat products, the percentages were not that much better than for eggs.
Why did the price of eggs rise so much more than for other basic foods?
Some possible reasons I've thought of are (1) people started eating more chicken because of the shortage of meat or (2) other areas of agricultural production were prioritized. However, I've found no evidence for either. In fact, for the latter, the opposite may have been true as people were allowed to keep chickens (and pigs) in allotments.
Another possible reason might be that demand for eggs rose sharply because of the high protein content, but the only evidence I've found for this is this article, The National Egg Collection for Wounded Soldiers and Sailors 1914-1918.
One source which might provide the answer is Peter Dewey, British Agriculture in the First World War but Google books doesn't allow much searching in this case.