The Supreme Court of the United Kingdom has ruled that a no oral modification provision in a written contract (a.k.a. amendments must be in writing) is enforceable. (See generally the Common Draft discussion of such provisions.) The supreme court reviewed precedent and statutory law from several jurisdictions, including the U.S. (e.g., quoting Judge Cardozo’s famous 1919 Beatty v. Guggenheim Exploration opinion), but concluded that there was no good reason not to enforce amendments-in-writing provisions:
12. … No Oral Modification clauses like clause 7.6 are very commonly included in written agreements. This suggests that the common law’s flexibility [about allowing contracts to be made and modified informally] has been found a mixed blessing by businessmen and is not always welcome. There are at least three reasons for including such clauses.
The first is that it prevents attempts to undermine written agreements by informal means, a possibility which is open to abuse, for example in raising defences to summary judgment.
Secondly, in circumstances where oral discussions can easily give rise to misunderstandings and crossed purposes, it avoids disputes not just about whether a variation was intended but also about its exact terms.
Thirdly, a measure of formality in recording variations makes it easier for corporations to police internal rules restricting the authority to agree them.
These are all legitimate commercial reasons for agreeing a clause like clause 7.6.
I make these points because the law of contract does not normally obstruct the legitimate intentions of businessmen, except for overriding reasons of public policy. Yet there is no mischief in No Oral Modification clauses, nor do they frustrate or contravene any policy of the law.
13. The reasons advanced in the case law for disregarding them are entirely conceptual. …
Rock Advertising Ltd. v. MWB Bus. Exchange Centres Ltd.,  UK 24 (emphasis and extra paragraphing added).
The supreme court did allow for the possibility that a party might be estopped from denying the validity of an oral amendment or -modification by another party’s detrimental reliance on the first party’s oral agreement to the amendment. The supreme court agreed with the court below, though, that there was no estoppel in the case at bar; besides, said the court:
16. … the scope of estoppel cannot be so broad as to destroy the whole advantage of certainty for which the parties stipulated when they agreed upon terms including the No Oral Modification clause.
At the very least, (i) there would have to be some words or conduct unequivocally representing that the variation was valid notwithstanding its
informality; and (ii) something more would be required for this purpose than the informal promise itself ….
Id. (citation omitted, extra paragraphing added).
EDIT: See also Glenn West, Cognitive Dissonance in the Common Law of Contracts: Oral Modifications to Written Agreements that Purport to Invalidate Oral Modifications, Weil’s Global Private Equity Watch, May 29, 2018, at https://goo.gl/vnGVQ1