You can VAT register whether you are an incorporated company or not. However, Customs and Excise takes a dim view of bodies registering for VAT purely for the purposes of saving themselves money. If they see that your input tax and output tax are vastly different (which is what yours would almost certainly be), they will start asking questions and probably want their money back. Bear in mind that they can get very nasty!
Another point to consider is that if you VAT register, although you will be able to reclaim the VAT on fuel and maintenance, you will also need to charge yourselves VAT on your hourly flying.
In my view, setting yourselves up as a company only really makes sense if you are going to be offering your aircraft for hire. You do not need the protection afforded by limited status unless you are exposing yourself to possible liabilities. If you are a closed group, limited status will not give you much protection against being sued or prosecuted.
I am a director of an aircraft operating company which hires its aircraft out. Our annual turnover is below the compulsory VAT registration threshold, and we took the decision not to VAT register as it would have made our hourly hire rate less attractive to customers.