So I think you might be conflating a couple things here.
First there's no reason a sole prop can't look super professional with smart branding and a good trading name. You can even have a VAT number in your personal capacity, but trading-as. So, many clients won't even realise you are not a company.
But nevertheless if clients are hesistant to do business with a one-man band that might be more because they are concerned about execution risks i.e. you getting hit by a bus, and not the corporate structure per se. IMO if they're being smart, they should prefer a sole-prop to a single-employee-company for legal reasons. But more than either of those they prefer to work with a team of 5+ people with inherent redundancy so that if one guy goes awol the project can still be completed.