My boss has asked me to invent and invoice (with no VAT)? Is this legal?

Absolutely not.

Do you have an email or a memo from him telling you to do it?

If you have it in writing, you have proof of him asking you to do something criminal...

If this is a small company run by him, get out of there and find another job. Interview with the new companies on the basis of career growth, and the possibility of more advancement. Stall over a reference from the present company, but just get out as soon as possible. You DO NOT want to be associated with them any more.

If this guy is willing to blatantly ask you to falsify a government document and cheat on the VAT, he is going to drag you down with him. Just quickly and quietly make your exit, and then speak to a lawyer first to keep you safe, and turn him in if you have written proof of the activity.

Examine the invoices you have on your desk,and make sure this isn't already happening. You don't want to be involved - you could go to jail. If you find any, go see a lawyer to protect you, and ask for whistleblower status.

No it is not legal, certainly not if the company is VAT registered and the invoice is subject to VAT so the 'invention' is tax fraud and more importantly VAT fraud

No it isn't. Inventing an invoice with or without VAT is illegal, especially if you are a registered for VAT company.