But they are all of the 1366 x 768 resolution. I am after 1920 x 1080.
What you're after doesn't exist. It's down to economics, I'm afraid, because the requirements fall between two stools.
For anyone looking for a TV, when viewed from the sort of average distance for a lounge / kitchen / dining room / bedroom the panel resolution difference between 1366x768 and 1920x1080 makes no appreciable difference when watching SD or HD content. However, it makes a fairly sizable difference to the product cost, and that's a problem. The average TV buyer would rather not spend the extra £50-£80 premium for a Full HD panel, so the manufacturers have no incentive to produce it.
Where someone is looking for a desktop-monitor-cum-TV -
and they know enough about specs to sort the wheat from the chaff - the panel quality in TVs just isn't up to the job. For a start, TV grade panels have too slow a pixel reaction time (GTG) which means ghost trails on screen. The bigger problem though is colour banding. A lot of cheaper panels are not true 8-bit. They're 6-bit plus 2-bit-FRC which is a cost-cutting measure. The bottom line for these is that proper 1080p computer monitors are cheaper and work better for PC use than some compromised crossover product.
There's also a commercial aspect to this from the panel manufacturers side. The LCD substrate is made in large sheets and then cut to size. There are several aspects to this: The size of the sheet that the plant can produce; the generation of glass it's making (less demand and hence lower unit profit for lower-performing glass such as 6bit + 2bit FRC); how many panels at a certain size can be cut from the sheet; the cost of maintaining older plant versus replacing it with something that produces a more valuable product.
The conclusion to all this is that if you want a Full HD screen, you have a better chance with a 32" size TV, but even they're thin on the ground.
So it seems that nowadays you have to compromise at least one of the items on the OPs list.