"They have damaged the trust and respect that I have built up over 14 years in the Welsh Parliament with my colleagues and the wider Conservative Party but more importantly with the people of Wales."
Darren Millar MS also announced he is stepping down.
Labour's Alun Davies MS has also apologised fro drinking at the Senedd during the ban, and has been suspended by his party.
"The regulations in place at the time imposed strict restrictions on members of the public with regard to the consumption of alcohol," said
"Given that the possible breach in question occurred as a result of the consumption of alcohol by Members of the Senedd, I have also written to the Standards Commissioner to ask him to investigate whether these Members acted in accordance with the duty in the Code of Conduct to conduct themselves in a manner which maintains and strengthens the public's trust and confidence in the integrity of the Senedd."
Wales is currently under alert level 4, which means hospitality venues must be closed apart from for takeaway and delivery.