ML-based Phishing URL (MLPU) detectors serve as the first level of defence to protect users and organisations from being victims of phishing attacks. Lately, few studies have launched successful adversarial attacks against specific MLPU detectors raising questions on their practical reliability and usage. Nevertheless, the robustness of these systems has not been extensively investigated. Therefore, the security vulnerabilities of these systems, in general, remain primarily unknown that calls for testing the robustness of these systems. In this article, we have proposed a methodology to investigate the reliability and robustness of 50 representative state-of-the-art MLPU models. First, we have proposed a cost-effective Adversarial URL generator URLBUG that created an Adversarial URL dataset ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Adv_\text{data}$</tex-math></inline-formula> ) . Subsequently, we reproduced 50 MLPU (traditional ML and Deep learning) systems and recorded their baseline performance. Lastly, we tested the considered MLPU systems on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Adv_\text{data}$</tex-math></inline-formula> and analyzed their robustness and reliability using box plots and heat maps. Our results showed that the generated adversarial URLs have valid syntax and can be registered at a median annual price of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\$}$</tex-math></inline-formula> 11.99, and out of 13% of the already registered adversarial URLs, 63.94% were used for malicious purposes. Moreover, the considered MLPU models Matthew Correlation Coefficient (MCC) dropped from median 0.92 to 0.02 when tested against <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Adv_\text{data}$</tex-math></inline-formula> , indicating that the baseline MLPU models are unreliable in their current form. Further, our findings identified several security vulnerabilities of these systems and provided future directions for researchers to design dependable and secure MLPU systems.