The law doesn't and can't force unmarried partners to support each other financially
Yes it does, as kickme illustrates, through regulations arising from legislation on welfare benefits and family law.
It means you don't have anybody step in when you, say, lose your job. Which may well be the case even if you have a partner.
If someone chooses to live with a partner who can't step in and help through hard times, then they're not much of a "partner" - but that's a matter for the individual, not the government.
The DWP's definition of a benefit unit is:
A single adult or a couple living as married and any dependent children.
So if you live with a man as husband and wife you cannot claim to be single without committing benefit fraud.
From a recent DWP Press Release:
People who tell the DWP they are single parents to get Income Support and Jobseekers Allowance, but are actually secretly living with someone as husband and wife, cost the taxpayer nearly £100 million in overpaid benefits, making it one of the most frequently committed benefit frauds. Just ten recent cases have cost the taxpayer over £1 million.
Ministers are also warning women that it is often they who face prosecution as the claims are invariably in their names. Despite their partners often encouraging the fraud, they often escape punishment.
You can read the whole thing, including the penalties for benefit fraud here.