Logburner cost?!

[Hairybaker]

Looking at this as a possibility, we don’t have a chimney and the wall it’s on is in our neighbours garden if that makes sense?! What would our flue options be and any rough idea of costs?!

You wouldn’t be able to have the flue discharging into your neighbours garden without consent.
In this situation I wouldn’t consent, the one my neighbour has discharging through his one storey roof stinks our house out and fills our bathroom with smoke! We are detached and have a lawn between us.
You would be best to get an engineer round and see what the options are re going through your own roof so they can say if a) it is possible & b) what the costs are likely to be.
Although why anyone would want one is beyond me
www.theguardian.com/environment/2021/jan/01/avoid-using-wood-burning-stoves-if-possible-warn-health-experts
Dr Nick Hopkinson, medical director at Asthma UK and British Lung Foundation, said both indoor and outdoor pollution caused by wood burning stoves caused serious health issues, from breathing problems to an increased risk of heart attacks, strokes and lung cancer.