The school are really tying themselves up in knots over this.
The child has an EHCP, a funded 1-1 and written confirmation from Medical Professionals that there is no reason why the child cannot go on the trip.
The school are saying that the child requires 2-1, this is the schools problem to solve not that of the OP.
The school are also saying that the TA is going to be used for the general staffing ratio, therefore will not be going for the sole purpose of supporting the child as per the EHCP so the child won't have 2-1 support anyway even if the OP goes (which she can't do).
This is direct discrimination, a direct contravention of Equality Act 2010, and is maladministration.
If the child remains in school then they must provide an alternative 1-1, if they don't that is also maladministration
If the school state that they don't have a TA to support her 1-1 and she can't go to school, then that is also maladministration.
This needs challenging.
OP, take a look at the IPSEA and SOS!SEN websites they both have good advice and model letters and the relevant sections of the Equality Act that you can use to challenge it, in the meantime email the head confirming what has been said, start the complaints process now, this starts a paper trail which you will need to escalate this through the correct channels, your dd has potentially another 3? years at this school and if you don't challenge it then it will continue.
I had exactly the same issues with my Son's school 10 years ago (direct discrimination and victimisation).
Initially they took him on trips with his 1-1, then said that he couldn't go unless I went at the same time removing his 1-1 to use her as general staff - child ratio, then refused to take him unless I transported him to/from the location in my own car, then they refused to allow him on the trips altogether whilst also saying that he couldn't go into school instead because their was no TA for him (at this point he was funded for 32.5 hours per week and had extra funding for 2-1 when necessary). Their arguments for this discrimination were weak to non existent.
Good luck OP.