I did notice that black outs are not happening every time but random.
Unless lights of the room are actually dimming it can't be actual black out or "brown out".
Active-PFC power supplies (if fully functional) commonly work down 100V AC voltage and that would cause major dimming of lights.
(without that there's likely no voltage variation which would trigger UPS to switch to battery operation)
So it's most likely some transient or other interference.
But switching power supplies themselves would be major sources of interference which is why they have line filtering section as first parts.
Besides keeping down the amount of interference they can transmit to AC line that also filters incoming interference.
So maybe that TV's power supply might not be in good shape.
Some grounding problem might also increase vulnerability to interference.
UPSes typically have also some transient/interference filtering, obviously no doubt worser in cheapest UPSes.
(just like in PSUs)
Now can I get one that will fulfil my need for £100/£150?
With needed power output that's tougher for even basic UPSes.
At least frombigger brands.
Not much point in UPS if it can't actually handle real black out without overloading.
So 1000VA/~600W would be good minimum.
Output wave form of UPS is another thing.
Switching power supplies actually rectify AC to DC (+filter it with capacitors) and then use that as power source for actual low voltage making transformer.
So theoretically they really shouldn't care much if input is some square wave or sawtooth wave or what ever.
But they're likely still built on assumption that AC input is sinusoidal liking that best.
And Active-PFC is also made to keep current draw follow voltage smoothly instead of having short sudden current spike (drawn by capacitors) during AC voltage peak.
So for actual black out/notable voltage sagging situation sinewave UPSes don't cause issues with more sensitive devices.
Cyberpower has cheaper sinewave UPSes than APC or Eaton.
Not sure how they keep price that much lower.
Smaller battery capacity alone shouldn't explain that.
And even with (modified) square wave UPSes would looks cheaper models carefully.
Besides line filtering things like durability might be bad.
For example APC Back-UPS ES is basically designed to bake itself from alive and also uses cheap garbage capacitors.