It's possible for sure and I'm equally sure that the helo company will be pleased to issue you a VAT invoice. The only question is whether the tax man takes the view that your paying for the hire through the company is relevant.
For example, if you are hiring a helicopter to attend a business meeting (or a series of business meetings), they will probably grill you, but let it pass. If you are taking a customer out for lunch, they will probably let it pass (but be prepared to provide full details of who/when/why). If you're taking the missus out to lunch (assuming you can't call it a shareholder meeting) or just poncing about on your own, they will note that down and charge you with taking a benefit in kind and fine you for not disclosing.
Generally 'tax man' and 'helicopter' are not good bedfellows. They were all over me like a rash when they found out about my machine. Fortunately I was ok there, but they did go through all my books with a fine toothcomb and got me on a number of other areas. And be very careful if you want to buy a helo through your company.......that's a whole different thread.