Actually, the parent you are assessed on depends on their status for the academic year you're applying for, not the past financial year. For example they could've been together for the whole tax year, and split in the August before you start. Only one parent would be assessed in this case.
Likewise, a parent could've been single for the financial year being assessed, but a partner moves in with them before the September you start. The partner also has to have their income assessed, but based on that previous tax year when they were not living together.