The phrase without fear or favour means: without pressure from, or partiality to, any person or other external influence.

This phrase occurs, for example, in Met police chief says two-tier policing claims are ‘complete nonsense’—video, published in The Guardian (London and Manchester, England) of Wednesday 7^th August 2024:

The Metropolitan police commissioner, Mark Rowley, has said accusations of two-tier policing are ‘complete nonsense’ and that those making the claims were putting officers at risk. ‘We stand in the middle, we operate independently under the law, without fear or favour,’ he said. ‘If you’re a keyboard warrior, you’re not safe from the law if you incite violence’.

The earliest occurrences of the phrase without fear or favour that I have found are as follows, in chronological order:

1-: From A Review of the Councell of Trent. Wherein are contained the severall nullities of it: With the many grievances and prejudices done by it to Christian Kings and Princes: As also to all Catholique Churches in the World; and more particularly to the Gallicane Church (Oxford: Printed by William Turner, 1638), translated from French by Gerard Langraine [Chapter 9, page 47]:

The Emperour Ferdinand hath said as much in termes so expresse, in a letter of his writ to Pope Pius the fourth, as takes away all scruple which can bee made hereof. That it may be lawfull (saith hee) for the Fathers, freely to speake and decree that which the Holy Ghost and their own consciences shall suggest unto them without feare or favour, all good order being there observed, by which meanes all confusion which might be feared shall be avoided, so as there shall be no need of running out of the Councell for the determination of such points as are debated in it.

Note: In the original French text, Reuision du Concile de Trente, contenant les nullités d’icelui: les Griefs du Roy de France & autres Princes Chrestiens: de l’Eglise Gallicane & autres Catholiques ([s.l.]: [s.n.], 1600), by Guillaume Ranchin, the phrase is “sans crainte & sans respect” (i.e., “without fear and without respect”) [Chapter 9, page 110].

2-: From A Prayer for the present times. 1642, published in A Manuall of Devotions, Suiting each Day; with Prayers and Meditations answerable to the worke of the Day. As also Each Man Calling, viz. The Noble man, the Soldier, the Lawyer, the Tradesman, the Seaman, The Sickman, the Dying man, &c. with answerable Prayers and Meditations (London: Printed by R. H. for George Tomlyn, 1643), by Thomas Swadlin (1600-1670) [page 536]:

For that Jesus sake blesse the Magistracy of this Kingdome, that they remembring the Judgement is not mans, but Gods, they may deale uprightly, without feare of favour, betwixt party and party.

3-: From An Exposition with Practicall Observations upon the three first Chapters of the Book of Job (London: Printed for Henry Overton, and Luke Fawne, and John Rothwell, 1647), by Joseph Caryl (1602-1673) [Chapter 3, page 326]:

To open the mouth and speake, is to speake boldly and confidently, to speak with freedom and liberty of speech; (as the Greek word signifies) to speake all a mans minde, without feare or favour of any man.

4-: From The Proceedings of the Parliament upon the Petition and Appeal of Josiah Primat of London, Leatherseller (London: Printed by John Field, Printer to the Parliament of England, 1651) [page 1529]:

May it therefore please the Parliament, in respect to the Publique Justice of the Commonwealth, to cause the Truth of the Premises to be speedily examined, and to provide for your Petitioners relief from the Oppression and Tyranny of the said Sir Arthur Hesilrige; and for the Dispensation of Justice, without Fear or Favor, as to your Wisdoms shall seem most just.
And your Petitioner shall pray, &c.
Josiah Primat.

5-: From The Protectors Protection: Or, The Pious Prince guarded by a Praying People. A Sermon preached at St Edmunds Bury in Suffolk, upon the 13 Octob. 1658 (London: Printed by T. J. for Wil. Fisher, 1659), by Samuel Slater (died 1704) [page 50]:

Princes stand in need of your prayers, because they are but men. Indeed they are men in an higher place, men in a greater letter, men of larger signification then others, yet they are but men still. It is true, the Lord hath said they are Gods, because they be his Vice-gerents, are clothed with his authority, and because they are to act for God, to do his will, and to seek his glory, and because they should act like God, holily, justly, righteously, without fear or favor, without partiality.

6-: From The Preachers Precept of Consideration: Or, Englands chief Lesson and Duty in this sad time of Visitation (London: Printed by E. Cotes for the Author, 1665), by Jeremiah Dobson [page 24]:

I shall (God willing) use all faithfulness and impartiality without fear or favour: for which end, I shall not trust to mine own private judgement, nor yet follow the partial Opinions, and censorious Fancies of others.

7-: From The Exact Politician, Or, Compleat Statesman: Briefly and Methodically Resolved into such Principles, whereby Gentlemen may be Qualified for the Managment of any Publick Trust; and thereby rendered useful in every Station to the Establishment of the Common Welfare (London: Printed for Dorman Newman, 1670), by Leonard Willan [Chapter 16: Of His Election, page 42]:

We first must agitate on His especial Election, which soly and immediately depending on the Arbitrament of a Prince or State, the success only rests in their Direction: to which, since the capacity of Judging in a Prince, is oftentimes obstructed by his proper inclination, Others Intercession, or by a remote, reserv’d or disguis’d Communication. It were far safer to require the Presentation of His Minister from the concurrence of the Society, to which he is to be a Member, under adjur’d Prescription, That without fear or Favour, they shall impartially propound no Person to his Trust, for any other consideration whatsoever, then for the advantage they conceive he holds or’e other in His Sufficiency and Integrity.