I almost feel sorry for them in a way. They'll have loads of distant relatives and old friends coming from nowhere, and be expected to sort out everyone's financial woes.
I would definitely opt for no publicity. Not that I do the Lottery anyway.
Prudie, the winners don't have a choice regarding the initial publicity created by the Lottery Corporation: it's part off the "fine print" concerning winning.
///If they have requested to remain anonymous, Camelot takes its obligations and duty of care to protect winners’ privacy very seriously. Unless a winner agrees to take full publicity and signs an agreement to that effect, no information about them can be released by Camelot into the public domain.///