You need to look at the wording in the EHCP.
If 1:1 is detailed, specified and quantified in F of the EHCP, it must be provided and can be enforced. Follow up the verbal conversation with an email. Remind the HT the EHCP is a legal document. Also contact the LA because ultimately it is their responsibility to ensure the provision is provided.
However, if 1:1 is not detailed, specified and quantified in F of the EHCP and the wording is vague and woolly (e.g. using words such as ‘access to’, ‘would benefit from’, ‘would be helpful’, ‘opportunities for’), it cannot be enforced. If this is the case you can request an early review with the intention of tightening up the wording.
If it needs to be a consistent person or the same one or two people sharing the role of providing 1:1 (e.g. one providing 1:1 in the morning and another in the afternoon), it needs to be included in F.
LAs and some schools like to misrepresent the research (most commonly Blatchford et al., 2012 and Sharples et al., 2015) on TAs. Michael Charles, a well regarded SEN solicitor, wrote an excellent piece on it. A well trained TA, deployed correctly does not lead to dependency.