What's BIK to do with whether or not it's a Limited Company? You can get clobbered for BIK on any business entity, not only that, if you are VAT registered then any supply to yourself is subject to VAT as well. There's no point in setting up a UK Ltd Co to try and save on tax or VAT because you only invite investigation. Where it would score is in limiting your liability. In the main, providing there has been no fraud or other illegal trading the shareholders liability is limited to the value of their shares. However the corollary of this is no-one in their right mind gives credit to a Ltd Co whose total capitalisation is ten shares of £1 each.
It helps if you go back to the origin of companies, which arose as a means of financing expeditions to foreign parts. It was a "Company of Adventurers" that would be set up to finance an expedition. Subscribers would buy shares in the company and when it was wound up at the conclusion they would share in the proceeds in proportion to their shareholding. If a dividend was declared during the life of the company that would also be distributed in proportion to shareholding.
Edited to add that Whirly's right, but then shareholder benefits are also taxable.