Hello Kate.
This also happened to me although I saw the additional children in a group (narrative, vocab, social) rather than one to one.
I feel if it’s needs driven , eg children being seen by me individually are also considered and included by the SENCO where appropriate, then parents of children being seen on my private caseload can have the option to opt in/out of the school group or my private sessions.
Most opted in to both the group and private sessions which then allowed me to focus individual sessions on another targeted need or to further consolidate if required.
I think the main thing is for you and school to have the discussion and be transparent with the parents so there are no surprises.
Hope this helps.
Gill