Per Sir Jones Romilly, MR in Jones v Foxall (1852) 15 Beav 388 at pp.396-397:
…I find that the offers were, in fact, made without prejudice to the rights of the parties; and I shall, as far as I am able, in all cases endeavour to repress a practice which, when I was first acquainted with the profession, was never ventured upon, but which, according to my experience in this place, has become common of late - namely, that of attempting to convert offers of compromise into admissions of acts prejudicial to the person making them. If this were permitted, the effect would be, that no attempt to compromise a dispute could ever be made. If no reservation of the person who made an offer of compromise could prevent that offer, and the letters containing or relating to it, from being afterwards given in evidence, and made use of against him, it is obvious that no such letter would be written or offer made. In my opinion, such letters and offers are admissible for one purpose only, namely, to shew that an attempt has been made to compromise the suit, which may sometimes be necessary; as, for instance, in order to account for the lapse of time, but never for the purpose of fixing the person making them with any admissions contained in such letters; and I shall do all I can to discourage this modern and, as I think, most injurious practice.
In Rush & Tompkins v Greater London Council  AC 1280, at p.1299, Lord Griffiths said:
The "without prejudice" rule is a rule governing the admissibility of evidence and is founded upon the public policy of encouraging litigants to settle their differences rather than litigate them to a finish. It is nowhere more clearly expressed than in the judgment of Oliver LJ in Cutts v Head  Ch 290, 306:
"That the rule rests, at least in part, upon public policy is clear from many authorities, and the convenient starting point of the inquiry is the nature of the underlying policy. It is that parties should be encouraged so far as possible to settle their disputes without resort to litigation and should not be discouraged by the knowledge that anything that is said in the course of such negotiations (and that includes, of course, as much the failure to reply to an offer as an actual reply) may be used to their prejudice in the course of the proceedings. They should, as it was expressed by Clauson J in Scott Paper Co v Drayton Paper Works Ltd  44 RPC 151, 156, be encouraged fully and frankly to put their cards on the table … The public policy justification, in truth, essentially rests on the desirability of preventing statements or offers made in the course of negotiations for settlement being brought before the court of trial as admissions on the question of liability."
The rule applies to exclude all negotiations genuinely aimed at settlement whether oral or in writing from being given in evidence.
Per Lord Hope of Craighead in Ofulue v Bossert  UKHL 16 :
12. I think that the public policy basis for not allowing anything said in the letter to be used later to her prejudice provides Ms Bossert with all she needs to defeat the argument that the implied admission that it contains can be used as an acknowledgment against her in these proceedings. The essence of it lies in the nature of the protection that is given to parties when they are attempting to negotiate a compromise. It is the ability to speak freely that indicates where the limits of the rule should lie. Far from being mechanistic, the rule is generous in its application. It recognises that unseen dangers may lurk behind things said or written during this period, and it removes the inhibiting effect that this may have in the interests of promoting attempts to achieve a settlement.