LONDON — Two recent, high-profile stabbing deaths have reignited a debate in Britain over whether a nationwide decline in the number of police officers is behind an alarming increase in knifings.

The clash has divided the Conservative cabinet, with the home secretary, Sajid Javid, demanding millions of pounds in emergency funding for the police, and Prime Minister Theresa May rejecting a linkage between knife crimes and cutbacks in the number of officers.

Lost in the back and forth about the smaller police forces is another element — the stringent overall reductions in public spending under the government’s austerity program, analysts say.

For example, the police now spend hours answering calls involving mentally ill people and sitting with them in hospitals, work that had been done by agencies that have suffered their own funding cuts or been eliminated entirely.