If the importation into the UKicon is for 'personal' use then there is no import licence or paperwork needed - all that happens is that the carrier (lets say TNT) ship into their hub in Coventry, they contact you to say its arrived, you go with your FAC with an open slot for that calibre and ;pay up'
The costs are :
Import duty at 3.5% of the value
VAT at 15% of the total value (including shipping)

You then pick up your rifle, take it home and notify the Police as usual within 7 days.

On the Canadianicon side (reading the legislation) it looks fairly simple - its just a case of finding someone to do the paperwork.
When I looked at importing the freight cost was around $100.

Relevant Canadian legislation copied below :
Authorization for individuals who hold a licence to export firearms

38. (1) An individual who holds a licence may export a firearm if, at the time of the exportation,

(a) the individual

(i) declares the firearm to a customs officer in the prescribed manner and, in the case of a declaration in writing, completes the prescribed form containing the prescribed information, and

(ii) produces his or her licence and the registration certificate for the firearm and, in the case of a prohibited firearm or restricted firearm, an authorization to transport the firearm; and


(b) a customs officer confirms the documents referred to in subparagraphs (a)(i) and (ii) in the prescribed manner.


A full transcript can be seen by clicking the link :

Firearms Act
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