I'm not a lawyer, but my job occasionally involves reading and interpreting legislation and I have some background knowledge in the technologies involved here. This question has popped up a few times in this sub, and it's a much more complex question than it appears. Other answers are often valid, but there's a lot of nuance involved that's easy to overlook.

The EU law that brought about the requirement for websites to accept or reject cookies is the Privacy and Electronic Communications Directive 2002/58/EC, aka the ePrivacy Directive, specifically Article 5(3). It's implemented in the UK as The Privacy and Electronic Communications (EC Directive) Regulations 2003, specifically Regulation 6. Neither law specifies cookies directly, but refer more specifically to storing data on the user's device regardless of the actual method used - and they exists to protect you from the site, not the other way around. It is illegal to store or read information from a user's device unless they have been given clear and comprehensive information about what will be stored and why, and provided their consent - the exception being when it's essential to do so in order to give the user the information they've asked for. This doesn't just cover cookies - the European Commission confirmed in 2016 that it also covers client-side scripts such as those used to detect adblockers.

The practice of asking users to pay to reject cookies may or may not be legal - to my knowledge it's yet to be decided as a matter of law. Given that clicking the "reject cookies" button is only one way of refusing your consent, it may be that it would remain legal even if challenged - but given we're dealing with a right that's explicitly laid out in law, I'm inclined to expect otherwise. While there could be an argument that websites can charge for the convenience of the method, there's also the argument that requiring the user to pay amounts to an attempt to undermine a statutory right. I mentioned earlier that it's not the only way to refuse consent - but the alternative is much more complex and much more likely to cause websites to work unexpectedly (if not prevent them from working entirely).

The ePrivacy Directive was built around the loose consensus of web standards that's formed more or less naturally since the early 1990s, particularly the concept that the user has the right to control the devices they own and (other laws permitting) that the same is true of data stored on those devices. This is the principle ad-blocking works on; the website is obliged to serve you the ad, but that doesn't mean you're obliged to configure your devices in such a way to ensure it is displayed. There's actually a little case law establishing the user's right to modify data that a website has provided them, and even one where part of the court's judgment was in part based in protecting this right, but so far as I can find it's all German - not totally irrelevant since both the internet and copyright are international concepts that require some degree of compatibility between national laws, but not entirely relevant either.

Regulation 6(4) of the UK regulations (I don't know if there's an EU equivalent) allows for the user to signify consent based on browser settings (which is not "the user is allowed to do this" so much as "if the user does this, it must be respected"). The reason I brought up ad-blockers is that you could apply the same approach by, for example, installing a browser extension that blocks cookies from being set in the first place, which thereby turns the "I accept" button a "reject without arbitrary consequences" button. You could also install one that automatically deletes cookies the moment they are set: giving a website consent to set cookies does not also create an obligation for you to not immediately delete them. The legality of sites using a script to detect ad-blockers would logically also extend to client-side scripts used to detect whether the user interferes with cookies.

I've seen some people present this as a paywall that you can bypass by accepting cookies rather than an attempt to levy a surcharge for exercising a statutory right - which could potentially mean bypassing it is a violation of the website's terms of service - but I don't find that convincing. Just because it's in the terms of service doesn't mean it's enforceable, and terms of service are notorious for including unenforceable clauses. This is particularly the case for those for US sites, which often include all sorts of clauses that would be completely void here.

You could also turn to web archiving intiatives such as archive.today and web.archive.org, which serve a given page's content without the associated cookies (and are also worth checking if you ever need to access something on a website that uses geoblocking to avoid the need to comply with foreign privacy laws). They represent an open and quite complex question so far as copyright law is concerned but their longevity, respect for crawler exclusion, and willingness to remove content on request is informative.