If the mother got an ILR stamp in her passport in the 1990s- then child would likely be British automatically by birth.
The concept of automatic PR for EEA/Swiss citizens only came into existence in April 2006. If the mother has been continuously working in the U.K. since 1991 then she almost certainly did acquire PR on 30 April 2006. If the intention is to register the child under section 1(3) of the British Nationality Act it is not clear that the Home Office can demand a PR document as long as she can evidence acquisition of PR some other way. Similar thread recently:
british-citizenship/mn1-for-a-child-bor ... 38447.html
That said- if the mother wants to apply for British citizenship herself- she will need a PR Card from the Home Office.
Nothing is said about the child's father- is he British or settled in the U.K.? Child may potentially be British based on father's status or eligible for registration under UKF provisions (cheaper than MN1).
Additional option: Since child has passed 10th birthday and it's stated has been in the U.K. throughout, registration on Form T should be possible:
https://www.gov.uk/government/publicati ... zen-form-t
Most EEA countries will allow dual citizenship if the child registers as British but there are a few exceptions. Which EEA country is involved?
This is not intended to be legal or professional advice in any jurisdiction.