Is IELTS mandatory for Ireland visa approval, and is there an IELTS waiver for the UK for a Master's/Bachelor's?

It depends.

For Ireland, an IELTS score is typically required for admission, but the Irish government does not mandate a specific IELTS score for student visa approval. Most universities require IELTS 6.5 (no band below 6.0) for master's programs. Some universities may accept a Medium of Instruction (MOI) letter as an alternative, but this is not universal.

For the UK, many universities offer IELTS waivers if your bachelor's degree was taught entirely in English and you provide an MOI letter. However, for the UK Student Visa, you must still prove English proficiency - this can sometimes be satisfied by your English-medium degree, but requirements vary by university and program.