The problem is that "more irregular" is not well-defined.
Language works[1] in stacked layers a bit like the OSI model.
* Raw sound is interpreted as phonetic units
* These are then reinterpreted as phonemes according to phonological rules. For example, you perceive "butter" as being pronounced "b - uh - t - r", but, in American English at least, that "t" is pronounced more like a Spanish "r" than anything you would recognize in isolation as a "t".
* Phonemes are organized into morphemes (units of meaning, e.g. "happier" has two morphemes, "happy" and "er").
* Morphemes are combined into words according to morphological rules.
* Words are combined into sentences (or other types of utterance) according to syntax. Popularly when people say "grammar" they mean morphology + syntax.
You could talk about "regularity" or "irregularity" completely separately for any of these layers and even then you would have to carefully define what you meant and how to measure it. And it's not clear that English is particularly bad in any of them.
The phonology example I gave might sound weird but all languages have stuff like this and English is far from being the most confusing[2]. For morphology you could propose a standard like "frequency of verbs with irregular conjugation" (or nouns with an irregular declension) and point to the prevalence of verbs like "sing/sang/sung" in English, but these are not English specific; most Germanic languages have roughly the same set of these "strong" verbs. (In Icelandic, "to sing" = "syngja" but "he sung" = "hann söng", rather than something like "hann syngði" which you would expect regularly and which doesn't actually exist[3]). For syntax I don't have a clue how you would even begin to measure regularity or irregularity.
Another thing "irregular" could refer to is the writing system. But first of all, writing and [spoken] language are kinda separate things (and a huge chunk of languages have no writing system at all). We could start writing English with a totally different alphabet tomorrow and it would still be recognizable as English and not fundamentally different. This has actually happened to several languages in the past; for example, Korean was written with Chinese characters and now it is written with the totally unrelated Korean alphabet, but it's still Korean either way. Serbs today may write Serbian with either the Cyrillic or the Latin alphabet, but either way, it's still Serbian.
But even if we accept for the sake of argument that talking about writing systems is meaningful, English is still far from the most irregular. In Japanese for example, it is basically completely impossible to even begin to predict how to write a word if all you know is its pronunciation. And then there is diglossia: people in Egypt, for example, would believe that what they are speaking and what they're writing are both "the Arabic language", but the written form and the spoken form are so dramatically different in every way that from an objective perspective they are separate languages, a bit like how during the Middle Ages people spoke French, Spanish, etc. but wrote in Latin.
[1]: this is all a rough oversimplification
[2]: This Quora answer is pretty interesting: https://www.quora.com/Which-language-has-the-most-complex-ph...
[3]: I think, anyway. But I don't really know Icelandic so someone can feel free to correct me.