Unfortunately, you have to charge VAT if these businesses are both registered for VAT. However, the two businesses may be considered separate if you meet the following conditions on HERE: https://www.vatforum.co.uk/post/two-businesses-are-they-separate-for-vat-10143611?pid=1308610333&highlight=separate; in which case you should only register the business that has exceeded the VAT threshold.
The independent UK VAT forum