Students (Tier-4) wishing to extend their visa must have to proof their English Proficiency Level. They have to obtain at least 5.5 on each level for IELTS.
As an alternative, you can also take an English course which is equivalent to B2 Level
Anyone wishing to apply for Indefinite Leave to Remain or Citizenship must have to pass either Life in the UK test or ESOL Skills for Life Citizenship Course.
You have to gain either Entry 1 or Entry 2 or Entry 3 Level Certificate in order to qualify for ILR or Settlement.