For extending visa, Life in the UK is not required. (its for ILR/BC only)
You need to pass English A1 only that is approved by the Home Office. I would assume Pearson is not on their list of acceptable qualifications.
What English certificate did you use for the entry clearance? As the letter suggests, you may want to use that one.
Unfortunately, the Home Office English Qualifications list is frequently changing and you need to keep up to date with it. Their latest one is not just a minor revision, but they have completely done a new one from scratch removing most of the qualifications from the old list. (they are still good to use until 5 November 2015 if taken before 6 April 2015)
Here's more information on the English requirements:
https://www.gov.uk/remain-in-uk-family/ ... of-english