As long as the ESOL is on the OFQUAL register and was taken in the UK, it will be fine to use according to the
gov website:
Approved English language qualifications
You can prove your knowledge of English by having an English level B1, B2, C1 or C2 level qualification that’s one of the following:
an ESOL qualification at Entry 3 or higher (eg Level 1 or 2) on the Ofqual register taken in England, Wales or Northern Ireland
an ESOL qualification at Scottish Qualifications Framework levels 4, 5 or 6 awarded by the Scottish Qualifications Authority (SQA) and taken in Scotland
on the Home Office’s list of recognised English tests and qualifications
Some qualifications on the Home Office’s list will expire after 2 years. Your qualification will still be accepted as proof if you’re applying for citizenship, even if it has expired.
Furthermore, if you view the naturalisation application, where it states how you meet the KOLL requirement, there is a tick box option that states if was demonstrated for ILR after 28 October 2013, so no need to take another test again.