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Fair Value of Financial Instruments - Schedule of Fair Value Assets and Liabilities Measured on a Recurring and Nonrecurring Basis (Details) £ in Millions, $ in Millions	Jun. 01, 2019 USD ($)	Jun. 01, 2019 GBP (£)	Jun. 02, 2018 USD ($)	Jun. 02, 2018 GBP (£)	Jun. 12, 2017 USD ($)	Sep. 13, 2016 USD ($)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities, Amortized Cost Basis	$ 8.7		$ 8.5
Available-for-sale Securities	8.8		8.6
Interest rate swap agreement - asset \| £		£ 19.2		£ 19.9
Interest rate swap agreement - liability	38.1		37.3
Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest rate swap agreement - asset					$ 75.0	$ 150.0
Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities, Amortized Cost Basis	0.8		0.7
Available-for-sale Securities	0.9		0.9
Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities, Amortized Cost Basis			7.8
Available-for-sale Securities	7.9		7.7
Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Total			16.4
NAV \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Total	69.5		121.0
Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Deferred compensation plan	12.5		15.1
Total	13.4
Contingent consideration	0.0		0.0
Total	1.4		0.3
Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member] \| Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest Rate Cash Flow Hedge Asset at Fair Value	(1.2)
Interest rate swap agreement - liability			0.0
Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member] \| Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Mutual funds - equity	0.9		0.9
Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member] \| Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities, Amortized Cost Basis	7.9
Available-for-sale Securities			7.7
Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Deferred compensation plan	0.0		0.0
Total	0.0		0.0
Contingent consideration	0.2		0.5
Total	0.2		0.5
Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member] \| Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Foreign currency forward contracts - asset	0.0		0.0
Foreign currency forward contracts - liability	0.0		0.0
Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member] \| Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest rate swap agreement - asset	0.0		0.0
Interest rate swap agreement - liability	0.0		0.0
Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member] \| Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Mutual funds - equity	0.0		0.0
Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member] \| Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities	0.0		0.0
Money Market Funds \| NAV \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Money market funds	69.5		121.0
Money Market Funds \| Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Money market funds	0.0		0.0
Money Market Funds \| Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Money market funds	0.0		0.0
Other Current Assets \| Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member] \| Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Foreign currency forward contracts - asset	0.0		0.4
Other Current Liabilities \| Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member] \| Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Foreign currency forward contracts - liability	1.4		0.3
Other Assets \| Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities	8.9		22.7
Other Assets \| Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities	0.0		0.0
Other Liabilities \| Quoted Prices With Other Observable Inputs (Level 2) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities	2.2		0.0
Other Liabilities \| Management Estimates (Level 3) \| Fair Value, Measurements, Recurring [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale Securities	$ 0.0		$ 0.0