Depends which part of HMRC you are arguing with; VAT or personal/business tax. I am assuming VAT, but if not then ignore.
For VAT rcovery there is an "expert", a guy named Daniel Barlow. He works out of the Reading office of Deloitte, and his number is available if you PM me but the general office number can found on their website
Deloitte UK | Deloitte in the South East | Audit, Tax, Corporate Finance | South East England - Deloitte LLP
I believe he has had some significant successes! He may also know a direct tax guy (if that is your issue).
VAT recovery fight can take two lines. 1) Private use; and 2) your helicopter purchase is an "investment", not a business. There is a fine line to tread and "expert" help seems to be a must. HMRC attitude is based on Yatch purchases, which they applied to fixed wing, then moved on to Helicopters. HMRC are fond of quoting decided cases to show that you can't have the VAT back, but "forget" to tell you about the cases whicht he taxpayer won!