Tracey, those are encaustics which tend to be 18-20mm in depth, your wood will most likely be engineered ply if you have underfloor heating and depths vary 12mm upward. If one or the other substrate needs to be built up to accommodate the other that is possible. Be aware there will be some movement between the two, more so if you are using long boards, less with parquet, so consider how best to deal with any movement or expansion between the two. There are plenty of products available for this. Make sure your encaustics are sealed correctly. You could also find the cleaning regimen of the two finishes may be very different. Lithoflin for encaustics - and oil/wax for an oiled floor, that's not a great combination, so perhaps an easy maintenance wood might be better in the long run.

I am looking for frameless(thin) sliding patio door in my kitchen and living extension. Does anyone knows the manufacturer in the north east UK?

The Howdens website describes the door as 19mm thick mdf with a PET finish and a 0.8/1.5mm ABS edging, which means its a vinyl wrapped cut and edged door. As the door has a deep J groove handle profile the sides of the door are cut and edged with the 0.8 edging and the bottom has a 1.5mm edging (due to manufacturing limitations with J profile handleless doors). These are a cheaply made door and the finish of the edging around the handle profile can be quite poor and susceptible to water damage. Most of the J profile doors on the market that have a deep J handle are made from 22mm thick mdf which means that the handle groove is bigger for your fingers to fit and the back of the groove is thicker/stronger and they are finished in paint (so there's no exposed edges). Also with the Howdens door range, their end decor panels are only 16mm thick where as the majority of decor panels are 18mm or some at 22mm to match the doors or I have one of my suppliers offers decors even thicker at 28mm.

I assume you’ve tried B&Q? They do sell just doors if it’s still in manufacture. Otherwise there are plenty of door suppliers online and you just have to find the nearest match. You can get paint colour matched at B&Q if colour is not quite right. Found this one in their clearance sale which probably means stocks are very low.