Are we, by any chance, getting confused between Harry Dunn and the case of Alfie Evans (where the circumstances were indeed similar to those of Archie Battersbee)?
https://www.bbc.co.uk/news/uk-england-merseyside-43841547
The link kindly provided by MissTerious has certainly provoked my interest in the involvement of the "Christian Legal Centre." It seems from my initial reading of that link and a couple of sources it cites (including court transcripts) that the organisation seems to be sailing very close to the wind with its offers of legal assistance. For example, a link from its website is labelled "Need Legal Advice". This is somewhat strange when CLC is in a position neither to provide legal advice itself nor to instruct, on behalf of a third party, somebody who can. Its involvement is also a little mysterious in that its headline on its homepage says this:
" We’re here to safeguard the freedom of Christians to live and speak for Jesus Christ, and to provide legal support for those taking a stand for Jesus and the truth that flows from him."
Leaving aside whether or not they are in a position to legitimately provide "legal support" I have at no time seen any indication that Ms Hollie Dance (Archie Battersbee's mother) is in any way a committed Christian. The closest I have seen is in one report where she is quoted as saying that it is for The Lord to decide when her son dies, not the doctors.
Curiouser and curiouser.