As an ex "tax man" although I should point out that VAT is a Customs & excise tax I am curious as to why you think you should be exempt from VAT on training costs?
VAT is an input and output tax on goods and services in connection with a registered business. In the UK this is (with some exceptions) charged at 17.5%. The way it works is that you charge tax for the output of finished products and services and then deduct the input tax from the raw materials or services used to produce the end product or service. The difference is paid quarterly to Customs & excise (or reclaimed if the end figure is negative).
Why do you think your "Training costs" constitute an input tax ? If your business is as a professional engineer" this is personal expense which is not allowable as you know. If you also carry out flight instruction for a local flying school you are presumably working for them either as an employee or freelance. In neither case would the VAT on your training constitute an input tax. If you are collecting tax for your services in connection with flying, you can claim the direct input tax for those services but not the tax that put you in a position to offer those services in the first place.
This is not dissimilar from the Inland revenue rules concerning claims for training cost allowances. You can claim for costs you directly incur as a result of your employment provide those costs are necessary and wholly as result of your employment . for example you can claim the cost of medicals or renewals if your employer didn't meet these costs. However you cannot claim for costs that put you in a position to undertake that employment in the first place. For example you cannot claim for the cost of your ATPL training now that you have been employed by an airline.
From your own statement you say the Customs & Excise officer has advised you that "professional flying is a hobby". It sounds as if they are stating that in connection with your business it may well be. As with all matters concerning Tax and VAT it is best to get expert advice. That will probably mean paying for it. I would not rely on the opinions received on this board (including mine !)
In summary most individuals cannot claim VAT back for their professional Pilot training and being registered for VAT most definetaly doesn't allow an individual or company to claim VAT back for personal expense.
Not sure why you think this is "Rumours & News".