I would have said go to the end of the week, because the rent is not charged by the day.
Reg 79(8) says HB ends from the following Monday unless para (9) applies (not relevant here) or unless the claimant’s rent payments “fall due on a daily basis”. The claimant’s rent does not falkl due on a daily basis in this case, it is due monthly.
As for the amount of eligible rent in the final week, Reg 80(2) says the eligible rent is M x 12 /52 except where para (3) applies. Para (3) applies to:
(a) first week in a “week one yes” case
(b) mid-week change of circs under Reg 79, including the end of [b:bc5c42389e]daily[/b:bc5c42389e] rent liability
(c) change of address with no overlap
I would say none of those is relevant here, so my view is the claimant is entitled to one full normal week of HB for the week in which he moved out.