The "de minimis" principle is not a uniform one, but highly contextual. It has been found in both civil and criminal law (both of which are relevant to copyright), for analyzing causation, level of harm done, extent of breach of a contract, and procedural compliance such as strict application of time limits. There is not much commonality here apart from a general sense that "trivial stuff" can be ignored. In Halsbury's Laws of England, the principle is summarized as (vol 96, para 759, 2018 ed.):
Unless the contrary intention appears, an enactment by implication imports the principle of legal policy expressed in the maxim de minimis non curat lex [...] so if an enactment is expressed to apply to matters of a certain description it will not apply where the description is satisfied only to a very small extent.
Note the several cautionary phrases requiring interpretation!
Small crimes are still crimes, but you might not get punished for them in practice
There are de minimis-type principles in many contexts, but in criminal matters the "contrary intention" is usually present. The idea is that when something is made a crime, Parliament has explicitly decided that the thing is really bad, and so even minor examples of the thing ought to be covered.
In the criminal law, it's typical to find offences that don't specify a minimum harm done for somebody to be found guilty, but where that does affect the sentencing. For example, theft has no exceptions for stealing things that are not worth much - and prosecutors' charging guidelines give some examples:
Theft can cover a wide range of financial harm, from something as minor as stealing a paperclip to theft of goods worth millions of pounds. Financial loss is one factor which will be relevant to whether a prosecution is needed in the public interest but the impact on the victim of the theft of even low value goods can be significant. Examples of thefts of low value goods where a prosecution might well be in the public interest would include items of sentimental value or items loss of which causes significant inconvenience, such as house keys.
Stealing a paperclip is still a crime, just one that you're unlikely to be charged with, given that prosecutors have better things to do.
In the same way, criminal provisions of copyright law don't require proving a specific amount of monetary loss. The legislation does currently say that gain or loss has to be monetary, CDPA (1988) 107(2A), 198(1B), but the nature of these offences makes gain or loss difficult to estimate. See R v Wayne Evans  EWCA Crim 139 for a case, relating to operating a torrent-hosting site, finding that although the prosecution's estimate of financial loss to the music industry was "entirely notional",
[t]here was undoubtedly a real loss to the owners of the relevant copyrights and related performers. Further, quite apart from such loss as could be identified and quantified, such offending always has a wider detrimental impact on the music industry and its profitability: and the music industry is an important economic contributor to society. That detriment is none the less real for being difficult to quantify. As has, in fact, long been established in the context of intellectual property offending, an element of deterrent sentencing is justified in this context; not least also because of the difficulty in tracking down and investigating such offending.
In a similar way, there is no "de minimis" standard to apply to your example of copying a single page - although you may have all sorts of other defences. It would be relevant at sentencing. It's also true that criminal prosecution is unlikely to be pursued if the prosecutors judge the harm is minimal (but as just explained, they might also consider it worthwhile on other public policy grounds).
"Striking out" is about serious procedural faults, not about aspects of your opponent's case you simply don't like
For your phrase "striking down actions", the precise terminology of "striking out" relates to civil procedure, where you may apply for the court to remove a statement from your opponent's pleading (or the court may do so on its own). This is usually combined with an application for summary judgement, because whatever remains after the striking out would not be enough to justify a trial. In the Civil Procedure Rules, and in actual practice, this is only really done if there's been abuse of process or the case is absolutely hopeless (e.g. the claims are totally incoherent). Judges will have an eye to the litigation history and the general conduct of the parties. If everything is in order procedurally then the action is likely to proceed. For example, in libel, a statement must now cause serious harm to be considered defamatory (and so "serious" is bringing de minimis ideas into play), but courts have allowed claimants a lot of latitude about what this really means - giving them the chance to argue it in court, even if they lose in the end.
There is a counterpart rule in criminal procedure but it is much more limited, applying only to abuse of process. It is established in R v Latif  1 WLR 104 that
An infinite variety of cases could arise. General guidance as to how the discretion should be exercised in particular circumstances will not be useful. But it is possible to say that in a case such as the present the judge must weigh in the balance the public interest in ensuring that those that are charged with grave crimes should
be tried and the competing public interest in not conveying the impression that the court will adopt the approach that the end justifies any means.
The idea is that if the prosecution's case does not meet the standard of an "affront to the public conscience", then it will proceed. And even if there has been prosecutorial misconduct, judges have often allowed the case to go on (perhaps with certain evidence excluded) rather than stop it entirely. So as far as your scenario, this particular bit of procedure is not relevant: you don't get to argue that the case should be thrown out before trial on the grounds that the alleged crime was not very serious.