This probably stems from the more administration required when running a company. It seems to be assumed that this additional administration includes VAT registration. VAT registration is only required when your annual turnover reaches £73,000.
However, many businesses choose to be VAT registered. This can be a sole trader, partnership or limited company business. The reasons to choose to be VAT registered include benefiting from the HMRC flat rate scheme or being eligible for VAT repayments.
This myth may also come from the fact that businesses with low turnovers are less likely to be run as a limited company. This is because the additional costs such as accountants fees may outweigh the financial benefits of a limited company such as tax savings.