Green’s Dictionary of Slang

Wilson’s den n.

also Tony’s den
[10 Downing Street, then home to Prime Minister Harold Wilson (1964–70; 1974–6); later Tony Blair (1997–2007); presumably the name can be altered to fit the current incumbent]

(bingo) the number ten.

[UK]D. Potter Stand Up, Nigel Barton Scene 12: All the sixes, clickety-click. Number Ten, old Wilson’s Den. Nearly there — eighty-nine. Was she worth it? Seven and six.
[UK]New Society XII 16/2: You hear the clack of the bingo caller’s ‘clickity-click — 66’ and ‘Wilson’s Den — Number 10.’.
www.ildado.com 🌐 Bingo Nicknames [...] 10.. Downing street (UK Prime Minister’s address), Cock and hen (rhyming), Uncle Ben (rhyming), Tony’s Den.