I'm ignoring the accusation that these shots "look bad" which is pure opinion. I actually quite like the first ones, the second is just 'standard fayre' for this type of shot.
These are artistic decisions, made by the director or director of photography, and in no way are due to tape-fail, generational loss or poor film stock. They are conscious decisions.
They quite probably don't involve 'grease on the lens' or as that's otherwise known, a 'soft or diffusion filter'. Though it's a possibility, it can be done in-camera without one.
BTW, though this diffusion effect can be done by rubbing Vaseline on a lens, that's more likely for a stills lens costing a mere 2 or £3,000, it's a whole lot less likely when your lens is more in the region of £40,000.
The effect in the first two shots is known as veiling flare.
It happens when the lighting is high and behind the subject. If uncontrolled - or done intentionally, like Kubrick in 2001 and every sci fi movie ever since - it can produce additional reflections inside the camera body; stripes, circles and dots in rainbow colours across the frame. When this is done it's generally just called 'lens flare'.
Veiling flare reduces contrast in the image and makes the scene look slightly 'foggy' though it's not due to any fog in the air, it's created entirely inside the lens/camera body.
One additional factor is that bright back lighting causes the edges of objects to also be 'haloed' in light. This, combined with the veiling, is what makes the foreground subjects appear to 'glow' with un-sharp edges.
In itself it is neither a good thing nor a bad thing. In the hands of an experienced photographer/cinematographer/DoP it can be used to highlight or emphasise an aspect of a scene. I don't recall this scene, so I don't know what the DoP was trying to emphasise, but we could guess at "Ooh, it's a lovely sunny day!" It was obviously shot either near noon in high summer, or at the sun's zenith if spring or autumn. The foreground colours are very warm. Whether the warming was done with a simple white-balance adjustment, with filters or in post is impossible to tell.
One thing it most definitely wasn't - it wasn't an accident.
The crew will have been there all day. The time that scene was scheduled to be shot would be at the right time of day for the shot required. These things don't "just happen" they are carefully planned. If they'd really wanted different lighting, they'd have picked a different time, a different angle, or a different location.
They could even have reduced the effect by shading the lens a lot more - hold a large black 'flag' between sun and lens and a lot of that would be gone. it would still be back-lit, but it wouldn't have the veiling.
The last image is a smaller aspect of the same thing. [It's actually slightly confused by the fact the image you have is an interpolation between two frames - that's more likely an artefact of processing done after the broadcast version and wouldn't be in the original scene, as shot.]
It is probably emphasised by smoking the room to make it more noticable and not simply done in the lens itself.
Smoking a room adds 'depth' to it. It hazes the background better in smaller sets, allowing the subjects to be emphasised and the background to be de-emphasised. It additionally adds haze to any practical lighting [like the candles]. Bare candles don't actually look great in sharp focus in a scene. Their point light is too bright and rapidly-moving for the scene compared to the 'ambience' they add to that actual [apparent*] subject lighting, and they just become too distracting. Smoking the room just softens them nicely in-camera.
*You'll note the candles don't actually provide the warm lighting to the scene itself, which is from behind the Doctor, with a blue specular highlight from the other side.
Again, other than the confusing frame-doubling artefacts, this was not an accident.
See PhotographyLife - Understanding Lens Flare for a more detailed explanation.
Also EnvatoTuts - Lens Flare Trends! What Is Lens Flare and How to Add It? which even teaches you how to do it intentionally in post.
And a late find - a history of Lens Flare, claiming actually Cool Hand Luke in 1967 was the first to do it intentionally…
On smoking a room, I found these Smoke & Haze – Creating Cinematic Depth and Fog, Smoke, & Haze: The Swiss Army Knives of Cinematography Tools