Senior police officers are receiving “off-book payments” and secret perks totalling hundreds of thousands of pounds, including private school fees and cars for their spouses.

The Times has discovered that one chief constable heading a force of just 1,700 officers was paid a £74,000 top-up on his salary last year. Sean Price, of the Cleveland force, was paid a £50,000 “retention package” and an “honorarium” of £24,000, raising his income to £200,000.

The private deals, sometimes referred to as debentures or supplements, are negotiated with police authorities behind closed doors and paid over and above salaries agreed in national negotiations.

The incentives include generous relocation packages, satellite TV, home security and even “lifestyle coaching”. They are legal but largely hidden from the public. The Times has uncovered the scale of the practice.