According to CIC help center:
What third-party language tests will CIC accept as proof I have adequate knowledge of English or French when I apply for citizenship?
A third-party test is a test done by an organization that is not CIC.
We will accept third-party test results as proof of your language ability if it is from one of the following organizations:
CELPIP General (Canadian English Language Proficiency Index Program General test)
CELPIP General-LS - a two-skills (listening and speaking) version of the CELPIP General test
IELTS - General training - General training (International English Language Testing System)
Test d'Évaluation de Français (TEF) (in French)
Test d'Évaluation de Français (TEFAQ) (in French) or TEF épreuves orales – a two-skills (listening and speaking) version of the TEF
Diplôme approfondi de langue française (DALF) (in French)
Diplôme d'études en langue française (DELF) (in French)
Test de connaissance du français (TCF) or Test de connaissance du français pour le Québec (TCFQ)
We will not accept third-party test results that are not on this list, even if they are similar.
Visit the organizations' websites to learn how to write the exams. Since they are not run by CIC, we do not track when and where they are offered.
SO YOU CANNOT USE YOUR ESOL CERTIFICATE
I have the same certificate form UK and it didn't count when I applied, and the rules of language test haven't change.