The answer is to be honest!
Tell them the truth.
You bought it second hand from Mr. X.
It would help if you are SSR and it would be "essential" to have already filed your CG66 (these are things "they" can check, and the more of your story that is both documented and checkable, the better off you are).
When, and if they check your story, you are in the clear.
With a dodgy invoice, (and imagine just how shifty you will look and feel as you hand it over!) and one phone call the their UK equivalent and you will find yourself in The Bastille and the key's gone rusty!
For completeness, I ALWAYS go through the Red Channel at airports and declare everything. You will be amazed at the positiveness that this engenders, surprised at the things HM C $ E tell you about what you have bought, and stagerred at the minute amount of duty they then ask you to pay!
Just do it-you know it makes sense.