We have similar, but only realised it part way through fitting. So we've got a property we worked hard on getting a reasonable air tightness....then stuck a great big Stovax dual sided stove in it with the air inlet kit creating a 4" direct feed sat underneath it. Live and learn
The stoves worth it though, even if we live with a knock to the air tightness, and despite wibbling about it for ages... I have NEVER noticed a draft around it, even on windy days.
And with our total energy bills averaging out at about £150/month for a very large and sprawling bungalow, with very heavy usage and a large background drain, (server, CCTV, full networking setup, dehumidify in garage etc) ... I'm delighted all round!