Benefit cap reduction is taken from both Housing Benefit and Universal Credit for a family receiving both #2136

Problem

When a family is paid both Housing Benefit and Universal Credit and the benefit cap binds, the model takes the cap reduction twice:

• housing_benefit.py returns max(0, housing_benefit_pre_benefit_cap - benefit_cap_reduction);
• universal_credit.py subtracts the same benefit_cap_reduction from Universal Credit;
• benefit_cap_reduction sums both pre-cap amounts, among others, and subtracts the cap.

No family gets both benefits on main today, because the housing_benefit_eligible routes exclude families claiming Universal Credit. #1910 adds such a route, for specified or temporary accommodation. Its body calls this the unresolved "reduction-coordination issue".

Evidence (synthetic households, not survey records)

• Add the universal credit limb of the Housing Benefit passport #2133's review, round 2: a lone parent with four children paying £18,000 private rent in 2025, with HB alongside UC and a nil UC housing element. The reduction is £8,055.40, but it comes off both benefits: £16,110.80 in total.
• Stacked run of Add the universal credit limb of the Housing Benefit passport #2133 on a local merge of Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910: the same family shape in 2026, with £3,000 earnings. The UC passport raises HB before the cap by £671. HB after the cap stays nil, and UC falls by £671, so the family is worse off. Details are in ~/reviews/uk-hb-uc-passport-2026-10-04/impact/stack_summary.md.

Law (legislation.gov.uk /data.xml, read 2026-10-04)

• UC Regs 2013 reg 80(2A), from 7 November 2016 (SI 2016/909): "Where the welfare benefit is housing benefit under section 130 of the Contributions and Benefits Act, the amount to be used is nil." So in the UC cap, HB counts as nil.
• HB Regs 2006 reg 75F(1)(g): the HB benefit cap does not apply where "the claimant is receiving universal credit".
• HB Regs reg 75C(2)(a): where the dwelling is specified accommodation (reg 75H), HB counts as nil in the HB cap.
• Northern Ireland: UC Regs (NI) 2016 reg 80(2A) and the NI HB Regs Part 8A equivalents. Check their numbering.

Fix

• For a family receiving Universal Credit, apply the cap to Universal Credit only, with Housing Benefit counted as nil.
• Do not cap that family's Housing Benefit.
• Any receipt test must read pre-cap quantities (is_uc_entitled, universal_credit_pre_benefit_cap), never post-cap universal_credit: Universal Credit depends on Housing Benefit through the cap.
• This should be a no-op on main; check with an Enhanced FRS run. It should land before or with Abolish working-age Housing Benefit from 1 July 2026 (NI 1 October 2026) #1910.

Axiom: rulespec-uk#425 (benefit cap exceptions).