client refusal to pay TVA

Hello,
Previously you gave me lots of information and advice about the rules surrounding TVA. I’m predicting to exceed the lower threshold for TVA exemption in the autumn, possibly october. I work for a large company in the UK who employ me as an “individual freelancer” and pay a fixed amount for each assignment that I complete. My invoices are “self billing” in that I input the work I have completed into an online database and this automatically generates an invoice which they email to me every month. On this invoice is a space for VAT (TVA) which has been blank for now. I contacted them to inform them that I was approaching the threshold and would need to start charging TVA. As the invoices are generated by them I asked them what the procedure would be. However, they replied saying that all tax is my problem and that I should seek external advice about tax. In my contract with them it seems to state quite clearly that they should be producing a VAT invoice for me every month and that VAT should be charged at the prevailing rate when appropriate. I highlighted these sections but have yet to hear back. My question is, can a company refuse to pay VAT? Is this a problem that an accountant can look at or do I need a lawyer?
I’m worried that if I exceed the upper threshold that will effectively give me a 20% paycut next tax year if I have to pay the VAT burden myself.

Thanks,
Charlotte