Firstly VAT registration is per person (sole trader, company etc) and not per business. Hence these fall under one name – your sole trader business unless you set up a company or another form of “person” and keep the businesses separate.
Please take a look at VAT Notice 733: Flat Rate Scheme for small businesses; Section 4.8 “Businesses that fits into more than one sector”:
“If your business includes supplies in 2 or more sectors, you must apply the percentage appropriate to your main business activity as measured by turnover. If the limited cost business rate applies you must use this rate, see paragraph 4.4. Choose the sector for which your business gets the greater part of its turnover. Don’t split your turnover, or apply more than one percentage.”