It will be all down to the oil fired combi boiler, unlike gas, an oil combi boiler does not modulate, so it is a smaller than normal hot water store, so what you want to do is move the water store from inside boiler casing to outside, so it depends on the make and model how that is done.
My brother-in-law had a integrated system with LPG, wood burner and solar panels, the idea is simple,
but in practice rather complex, there must be room in the water store for the hot water produced, and solar panels and wood burners can't be simply switched off like a oil or LPG boiler, so he had twin large tanks, upstairs so power cut would not stop water circulating, and it did work well, he could go to Germany where his daughters live, and home was maintained while away with solar only.
But this was in a new build, and the floor was reinforced to take the weight, when he looked at fitting in an existing house after he moved, he found it would take over 25 years to break even on cost, and over 25 years interest charges on money used or lack of return as money not invested means they never will pay for them selves.
Clearly there is more than cost saving for you, but there is a huge difference between an emergency solid fuel fire, and a fully compliant fire which will not cause particular emissions, the main point is to stop particular emissions the fire needs an after burner of some kind, so flue gases get very hot, some where extra air is fed into the burner, I knew a guy who was very keen on natural forest practice and wanted me to write a website for him, first step was research, and when you look at the units being sold it seems there was a flaw.
The first two seem great, until you consider it needs electric, and emails asking what happened in a power cut failed to get a response, the third is the rocket mass heater which is home made, and presents a problem with house insurance. I have lived with solid fuel heating, as a boy in a steel works town we could buy small coke cheap as small stuff no good for steel making, to burn coke means doors on the fire, and the Aga stove had a side boiler, and I have needed to rake out the fire onto a shovel and take it outside when the water supply failed. Also run off hot water when it started to boil. The fires were efficient, but poor installation, there was no ducting to take combustion air from outside, so they caused drafts through the house, and parents used high backed chairs to stop draft hitting them.
There are solid fuel fires designed to take combustion air from outside, but cost is much higher, oddly referred to as open flue when air drawn from inside the home, even when the flue is clearly not open, it refers to source of combustion air. With an open flue one has to be aware of causing a depression within the home which can draw in combustion products, so bathroom extractor, cook hood, general kitchen extractor even a tumble drier can all cause a depression, using heat recovery units, and condensed dryer clearly help, but kitchen can be a problem due to grease build up.
I personally have an open fire and some wood for emergency use, normally a cover over the fire place and a connection to fit the air conditioning unit to the flue in the summer, never as yet lit a fire. Up to date used electric heating when oil boiler has failed. Whole idea of wood burner is when electric also fails, so any system needing electric to work seems pointless.
After seeing brother-in-laws set up I was sold, thought it was the bees knees, until I saw the price, same with things at the Centre for alternative technology the units shown seem great, until you look at cost, building a house with hay bails seems good, but needed electric lights as so dark inside.