Developing and maintaining automated tests for graphical user interface (GUI) applications remains costly, as test scripts are typically tightly coupled to low-level UI elements. Recent advances in large language models (LLMs) open new opportunities to execute test cases expressed in natural language (NL), potentially reducing the effort required to create and maintain test suites. However, delegating test execution to probabilistic LLM agents raises fundamental challenges for software testing, including ambiguity in NL test cases, unpredictable LLM agent behaviour and the lack of theoretical foundations for reasoning about NL test case execution reliability. This paper focuses on these problems and presents a NL test case execution algorithm that orchestrates specialised LLM agents to interpret and execute NL test steps in a controlled manner in order to limit false positives and false negatives. This algorithm includes guardrail mechanisms to mitigate uncertainty in language-driven execution. It combines grammar-based disambiguation of NL test steps, rule-based GUI readiness verification, and strict evaluation of assertions. To reason about the reliability of NL test case execution, we define the notions of weak unsoundness and weak laxness, which adapt classical conformance testing properties to the context of LLM agent-based testing. We implemented our approach in a prototype tool and constructed four NL test suites targeting six web applications to evaluate our approach in terms of weak unsoundness and weak laxness. Experiments with locally deployable open-weight LLMs (14B-70B parameters) show that, when paired with a high-capability model and under the conditions provided with our definitions, NL test cases can be executed reliably, they rarely reject conformant applications (false positives 1%) and rarely accept non-conformant applications (false negatives <4%). These results open the path toward treating natural language test descriptions as executable testing artifacts.