The remedy, avoid and manage wood tar.

Both of these problems were caused by wood tar. Both chimneys were cold and on an outside wall of unlined porous brick. As the flue gasses pass through the colder atmosphere they condense to form tar on the surface.

A good chimney liner would keep the gasses warm and help them move quickly to the outside. In the event of a fire in the chimney chamber, a properly installed flue can withstand the heat and will not conduct it to the chimney fabric.

The remedy, manage the wood.

This means that you must burn dry wood, never fresh or wet wood. The family with the Rayburn would 'bank down' the fire at night to save lighting it in the morning. This slow combustion exacerbated the effect and fumes became even more noxious.
Everyday you should burn a stove hot with ample air to heat up the chimney and crystallise the tars.

Build a well ventilated wood store, buy your wood at the beginning of the summer and store it for the winter. Ideally two years drying. Or make sure you buy seasoned wood from a reliable woodman.
You can buy electronic moisture meters from Maplin to assess the relative moisture in the wood. Some folk even weigh the wood before and after drying to compute the percentage moisture. Of course old scrap wood is ideal. It has a second life keeping you warm.

The remedy, regular maintenance.

Regular chimney cleaning will not only maintain the performance of your stove, it will ensure that you do not have a build up of soot and tar. Where possible, look down from the top and up from the bottom of the chimney for creosote deposits. A depth that exceeds 1/8 inch should be cleaned. We recommend that every homeowner have their chimney inspected, and swept if necessary, when they move into a home before using the chimney. Annual inspection and cleaning (as necessary) should be undertaken to ensure safety and maintenance of house insurance coverage. It is not difficult to access the chimney via the access plate and sweep the chimney with a stiff chimney brush.
If you can't do it yourself Green Man Stoves can provide a complete maintenance service for you.
Most wood stoves burn on the ash and should only need cleaning out when the build up of ash interferes with the burning.
We will advise you the best way to tune up your new stove. Gradually acclimatise the cast iron to the demands of the fire. Too much heat too quickly can harm your stove.

A cautionary tale.

From personal experience I can site two examples that nearly proved disastrous.
My neighbour lives in a picturesque thatched cottage. It has not been modified for many years and the family were cooking on a very antique open fire cooking range. To make life more efficient they removed the old open range and installed a Rayburn cooker in it's place. Blocking off the chimney with a register plate and adding a sweep access door on the outside. This all made perfect sense. The son had access to unlimited supplies of wood as he worked as a woodman. Every day a few more logs would arrive home from work.

Within six months the chimney on the old cottage was ruined. The flue gasses had condensed and deposited a thick gooey tar onto the inside of the chimney. The chimney gap was reduced to less than 75mm. It was impossible to push a chimney brush up the chimney. Of course the chimney smoked and the Rayburn, the old sort designed for solid fuel, would not gain temperature to cook.

The problem eventually forced a complete rebuild of the whole chimney stack, the bricks had become stained as the tar percolates through to the outside. Of course the fire hazard was considerable and if the tar had ignited the resulting chimney fire would have been catastrophic.

This happened to another cottage in the village. A wonderful house that had a deep and large inglenook. Ideal for a woodburner and again the DIY solution just added a register plate to vent the gasses into the very large chimney void. All was well for years until one day someone felt the wall above the mantelpiece, it was warm, very warm, even though the fire was out. The fire brigade was called, they smashed into the chimney void to expose a smoldering fire that was just about to break into the house. It had been burning for weeks. The resulting water damage and rebuilding costs were considerable.