The shareholders or owners may or may not receive compensation.
Presumably a normal(?) interpretation would be that the British government uses whatever eminent domain law it has and it takes over Adels copyright on all her songs and gives her whatever the fair market value of the catalog is.
But because this is a joke candidate, could be anything.
Water companies used to be publicly owned until Thatcher privatised them. Unfortunately, as they are a natural monopoly (you cannot choose which company to supply your water services apart from moving to a different part of the country), the companies have basically been extracting as much money as possible from the public and not investing in the infrastructure. This has led to ridiculous bills for water and disastrous performance in terms of not pouring sewage into waterways. The classic example is Thames Water which is now saddled with incredible debts and is asking for yet more money to invest in infrastructure (which they didn't do all the other times they asked for more money).
Generally water nationalisation means nationalising the companies which supply water to homes and businesses. Not, er, literally nationalising water as in the substance.
If we project her lifespan as 50 more years and assume the UK population stays stable at 70 millions, that works out at 3835 and a half lunches per day.
[0] not a lawyer [1] what does “nationalise” even mean?