This is not a hung (UK) Parliament. When Parliament meets a majority of those voting will vote for the Tory leader (although by that time PM May have stepped down).
With 649 of 650 seats declared at this juncture (10 AM BST, June 9, 2017), the Tories have 318 seats.
The three primary opposition parties, Labour (“Lab”), Liberal Democrats (“LibDem”), and Scottish National Party (“SNP”), have 261, 12, and 35 seats repectively. That is a total 308 seats. Add to the 308 the 1 seat not yet declared,** and that brings the opposition to 309 seats. Add 1 seat for the Greens, and that brings the opposition to 310 seats. Add 4 independents, and that brings the opposition to 314 seats.
318 + 314 = 632 (out of a 650 seat total)
That still leaves 18 seats for Northern Ireland (“NI”) to enter the mix. 7 seats went Sinn Fein (“SF”), the Irish nationalist party seeking to end the connection between NI and the rest of the UK. 10 seats went to the Democratic Unionist Party (“DUP”) and 1 seat went to an independent unionist candidate (in fact, a former Ulster Unionist Party or UUP member). The SF members will not take their seats and vote against the Tory Government—at least, they never have in the past. And if the SF members did take their seats and vote against the Tory Government, all that would happen would be that the DUP members and the independent unionist member would vote with the Tory Government. The likely result is that SF members will sit out any no confidence motion, and that the 11 NI unionist members will either not vote or vote for the Tory Government.
That leaves the Tory leader (Prime Minister May or her successor) with a 318 to 314 vote on a no confidence motion and a majority of 4.
QED: No hung parliament.
Addendum: It was announced that the DUP and the Tories have reached a deal. It is probable that DUP will support the government, but remain outside, and not take any ministries. But it is also possible that DUP will enter a formal coalition with the Tories. Either way, a no confidence vote will now be 329 to 314 (with 7 Sinn Fein abstentions). This is a majority of 15. [I am assuming that the one independent unionist member from NI will support the Tory government.]
**The last seat went Labour by 20 votes on the third recount. See http://tinyurl.com/yah4p86p
PS: As for the remaining undeclared seat, see Kensington count suspended without a result, Metro (June 9, 2017, 7:55 AM), http://metro.co.uk/2017/06/09/kensington-count-suspended-without-a-result-6696949/
PPS: Theresa May reaches deal with DUP to form government after shock election result, The Guardian (June 8, 2017, 07:05 EDT), http://tinyurl.com/yb57oefj
Citation: Seth Barrett Tillman, This Is Not A Hung Parliament, New Reform Club (June 9, 2017, 5:07 AM), http://tinyurl.com/ydckrxup