VAT being charged when not VAT registered

Hello Everyone

I’m just looking for some advice from anyone who has a reasonable knowledge of VAT.
I have been running a Limited company (VAT registered) for a few years now. Late last year I decided to do some part time work to earn some extra cash.
The part time work was different to my regular business. Initially for my part time work I did the accounting and bookkeeping with my limited company. I was advised that due to the two trades being different then it was best to operate as two different companies independent of each other.
I set up as a sole trader business (not VAT Registered) and I now operate my part time business through the sole trader business. I now receive payment into the sole trader business through a Business Bank account, which is different to my Limited Company Bank account. The part time income I receive is currently only from one supplier.
I have advised the supplier that my details have changed from limited to Sole trader. Despite this they have been sending me invoices with my initial limited company details and also adding VAT to the invoices. I do not raise the invoices they are self-billing.

I have emailed the suppliers on numerous occasions advising them that I am not VAT registered, and invoices should be sent with my new sole trader company details, and they have never responded to any of the emails. I cannot phone them as they do not have a phone number I can use.
Any advice would be appreciated,

Thanks