Schools are expected to make reasonable adjustments, but prohibitively expensive equipment which is not covered by the HNF/EHCP funds, left over after other, more conventional spending for her support, is not reasonable. Your LA should has a fund for this and are responsible for ensuring that your school has the funding or equipment provided, after all, they are the ones whose team assessed and issued the EHCP – they should know the needs.
Price up the other support the student will need and show what is left – if this does not cover the equipment (and I am guessing it won’t come even close!), then you are being expected to spend significant amounts of money allocated for the education and support of other students on this pupil – which is not how school funding should work. Your LA have got a process and fund for this, they may have spent it – but the onus is still on them to provide. Under your LA’s ‘local offer’ you should find information on the ‘Element 3’, ‘high needs block’ or ‘top up’ funding – this is the fund designed to support individual students who need significant additional funding for support beyond the reasonable expectation and budget of the school. If you can prove it is needed, you qualify. If they say they don’t have this fund or your school is responsible, this is not true.
It is horrible to have to fight like this, as we all want every pupil to access the school of their choice and the funding/LA should not be the stumbling block.
In my local area, the information for Element 1, 2 and 3 funding is shown in this doc: https://www.kent.gov.uk/__data/assets/pdf_file/0020/18731/IASK-funding-for-special-educational-needs-in-mainstream-schools.pdf