Per Lord Neuberger in FHR European Ventures LLP v Cedar Capital Partners LLC  UKSC 45 at paras 1 and 37:
1. whether a bribe or secret commission received by an agent is held by the agent on trust for his principal, or whether the principal merely has a claim for equitable compensation in a sum equal to the value of the bribe or commission. The answer to this rather technical sounding question, which has produced inconsistent judicial decisions over the past 200 years, as well as a great deal of more recent academic controversy, is important in practical terms. If the bribe or commission is held on trust, the principal has a proprietary claim to it, whereas if the principal merely has a claim for equitable compensation, the claim is not proprietary. The distinction is significant for two main reasons. First, if the agent becomes insolvent, a proprietary claim would effectively give the principal priority over the agent’s unsecured creditors, whereas the principal would rank pari passu, ie equally, with other unsecured creditors if he only has a claim for compensation. Secondly, if the principal has a proprietary claim to the bribe or commission, he can trace and follow it in equity, whereas (unless we develop the law of equitable tracing beyond its current boundaries) a principal with a right only to equitable compensation would have no such equitable right to trace or follow.
37. The whole reason that the agent should not have accepted the bribe or commission is that it puts him in conflict with his duty to his principal. Further, in terms of elementary economics, there must be a strong possibility that the bribe has disadvantaged the principal. Take the facts of this case: if the vendor was prepared to sell for €211.5m, on the basis that it was paying a secret commission of €10m, it must be quite likely that, in the absence of such commission, the vendor would have been prepared to sell for less than €211.5m, possibly €201.5m. While Simon J was not prepared to make such an assumption without further evidence, it accords with common sense that it should often, even normally, be correct; indeed, in some cases, it has been assumed by judges that the price payable for the transaction in which the agent was acting was influenced pro rata to account for the bribe
Per Lord Justice Longmore in Novoship (UK) Ltd & Ors v Nikitin & Ors  EWCA Civ 908 at para 2:
When Odysseus penetrated the underworld, he encountered, among many other ghosts, that of Eriphyle whom Homer (Od. 11.326) calls "hateful" because she had been bribed by Polyneices with Aphrodite’s golden necklace to reveal the whereabouts of her husband, so that he could be found and compelled to march on Thebes where he foresaw he would be killed. This may or may not be the first recorded instance of a successful bribe but, centuries later, bribery is still prevalent and pervasive however much legislators and judges try to stamp it out.
Per Smith J in Fiona Trust & Holding Corporation Ors v Privalov Ors  EWHC 3199 (Comm) at paras 70-73:
70.English law take a broad view of what constitutes a bribe for the purposes of civil claims. It considers that a bribe (or "secret commission" or "surreptitious payment") has been paid where "(i) the person making the payment makes it to the agent of another person with whom he is dealing; ( he makes it to that person knowing that that person is acting as the agent of the other person with whom he is dealing; an he fails to disclose to the other person with whom he is dealing that he has made that payment to the person whom he knows to be the other person’s agent": Industries & General Mortgage Co Ltd. v Lewis,  2 AER 573 at p. 575G. Thus, a bribe is "a commission or other inducement which is given by a third party to an agent as such, and which is secret from his principal": Anangel Atlas Compania Naviera SA v Ishikawajima-Harima Heavy Industries Company Limited,  1 Lloyd’s LR 166 at p. 169.
71. "When an agent receives or arranges to receive by way of a bribe or secret commission in the course of his agency from a person who deals or seeks to deal with his principal, the agent is liable to his principal jointly and severally with that person (1) in restitution for the amount of the bribe or secret commission; or (2) in tort for any loss suffered by the principal from entering into the transaction in respect of which the bribe or secret commission was given or promised, and the bribe, if it was paid, is held on trust for the principal", and the person who pays or promises the bribe is also liable in restitution and damages to the principal: Bowstead & Reynolds on Agency (2010) 19th Ed at 6-084. The principal may also require either the agent or the briber to give an account of profits.
72. It is not necessary in order to establish a claim for a claimant to show that the bribe was either paid or received dishonestly: where a bribe is paid, it is irrelevant whether either the briber or the agent realised that they were doing wrong. In English law corruption and fraud are presumed, and so a claim can be brought on the basis of the payment of an "innocent" bribe: Re a debtor,  2 Ch 367 at p. 376 per Scrutton LJ. It is also presumed that the person paying a bribe intended that the agent would be influenced by it and that the agent was in fact induced to act in favour of the briber in relation to transactions between the briber and the recipient’s principal: Hovenden & Sons v Millhoff, (1900) 83 LT 41; Industries & General Mortgage Co Ltd. v Lewis, (cit sup). If a bribe is paid to an agent, it does not assist the briber or the agent to show that in fact the agent acted in his principal’s best interests.
73. The reason that the law so protects a principal if his agent receives a bribe is that he is entitled to be confident that the agent will act wholly in his interests, and the test for whether a payment or other benefit or promise amounts to a bribe depends upon whether it puts the agent in a position in which his duties to his principal and his interest might conflict. Accordingly:
i) It is not necessary that the bribe be given in connection with a particular transaction or series of transactions. The possibility of a conflict between duty and interest might be created by a bribe paid to an agent in order to influence him in favour of the person paying it generally and not directed to any particular matter or intended to influence him in relation to a particular transaction. In the Fiona action the claimants have sought to link payments made to Mr. Privalov and Mr. Borisenko and arranged by Mr. Nikitin to particular schemes about which they complain, but, as I shall explain, I conclude that they have not established connections of this kind. This does not mean that they are not entitled to rely upon the payments as bribes. If a secret payment is made to an agent, it taints future dealings between the principal and the person making it in which the agent acts for the principal or in which he is in a position to influence the principal’s decisions, so long as the potential conflict of interest remains a real possibility: see Daraydan Holdings v Solland,  Ch 115 at para 132.
ii) The law recognises that some gifts or benefits are too small to create even a real possibility of a conflict of interest and so too small to be treated as a bribe. The defendants say that some benefits that Mr. Nikitin is said to have provided to Mr. Skarga and Mr. Izmaylov were of insufficient value to be bribes, and were only what Gorell Barnes J called in The "Parkdale",  P 53, 58-9 "a little present". It is a question of fact depending on the circumstances of each case where the line is to be drawn between "a little present" and a bribe, and so unsurprisingly there is little guidance about this in the authorities, but the test, as I understand it, is whether it is sufficient to create a "real possibility" of a conflict between interest and duty: Imageview Management v Jack,  1 Lloyd’s Rep 436 para 6 per Jacob LJ. It is not whether such a conflict is actually created.
iii) If a payment is made to an agent that creates a real possibility of this kind, it does not make "any difference whether the surreptitious profit was gained as a pure gift or for services rendered or for any other reason": Keogh v Dalgety & Co Ltd., (1916) 22 CLR 402, 418. An agent might have a conflict between his interest and his duty as a result of being rewarded for "moonlighting" for a person engaged in transactions with his principal.