To add to Dublinpilot's post, I now believe (could be wrong - always check with an accountant specialising in businesses of this type) that under the current aggressive "screw anybody with more money than me" Revenue approach to these types of "dual use" assets, the only way for one's business to own a plane, and not have the proprietor get done for BIK, while permitting the proprietor to do business flights, is to do an explicit agreement with the tax inspector first.
Then, private use will be OK too; you just agree a certain percentage, say 75% business / 25% private. With appropriate reimbursement of private flying costs to the company, this will avoid BIK entirely. We don't get to hear about this much because every businessman/pilot who has done this is keeping quiet about it.
The other way to avoid BIK would be for the proprietor(s) / Directors / employees to be contractually barred from using the plane for private purposes, and then you have to hire an outside pilot to do the flying.
There may be other ways for one's main business to own a plane, while not getting done for BIK, but I don't know what they are.