JB, Atkin has BV (brand value) level two (BV2) per the auction market.  BV2 has 3/4 the value of an "identical" gun of BV1 (Boss, H&H, Purdey, and Woodward).  Likewise it has 1 1/2 X the value of BV3.  The two other factors are Original Quality grade (OQ) and Current Condition level (CC).  
Atkin made a fairly high % of best work guns, so let's assume it is a best work gun, OQ1.  Properly restored with replaced barrels is usually a CC6.  
BV2-OQ1-CC6 = $6,655
That SWAG may well change with a more accurate assessment of OQ and CC.  
Post back with a description and, hopefully, photos.  Hope that hel[ps some and hope to hear more from you.  I'll fix the PM issue soon.
DDA