Extended from a comment above:
I say they pushed someone up there to paint it on a real aircraft, probably overnight or it was still wet when they pushed the camera around; and at the same time stuck a flag pole on it. Remember, you aren't painting the whole thing to aviation standards, just a small bit for the camera.
In fact, looking at it, it looks a bit warped. If not the curved tv screen or my eyeballs then the livery could conceivably have been a giant piece of painted fabric or paper tacked or glued on just for the shot. Even easier than painting onto the fuselage.
It seems like it would be overkill to paint an actual plane just to show it for a second or two.
Crew on productions like to do their jobs and do their best (jobs in the industry are often word of mouth - if you aren't seen to be doing your job then you won't get hired on the next one). Having worked on large and small productions, things that are not even seen on screen are still done even if it all seems a bit silly and superfluous (ie. costume parts that the camera will never see) are still tended to.
However, if its something that has a large effect on the budget available, then obviously common sense and special application apply (such as only building one side of a huge spaceship).
Note, the aircraft used in both shots (nose and livery) is a Hawker Siddeley HS 748 (or Andover in military service). Originally designed by Avro aircraft company, it was a medium-sized turboprop airliner that entered service in 1961.
By the date of 'Yes, Minister' production, 1980, it would be considered an old aircraft and perfectly acceptable to use and abuse.
Old aircraft are always available for filming (i've been on many jobs where they utilize old aircraft (one is on Netflix now!), some may still be in taxiing-condition (ie. they can power up and move but are not certified to fly, so just run up and down the taxi/apron) and modify what they need to , to get the job done.
What they need to do here is actually quite limited:
The nose livery is probably unchanged from whatever condition the 748 was in.
The flag and flag pole had to be added.
Only a small part of the upper livery is being affected. If the aircraft is a running/serviceable aircraft, it may well be a charter aircraft, ie. a company owns the aircraft, which is then leased out to an airline - until that happens the plane is a plain white livery with no names or other colors attached to it until the aircraft is confirmed to be delivered to that airline.
In this case the font and text applied is very simple, so it would not be inconceivable to get it done relatively quickly.
Since the HS 748 in this case seems to be running at least, all they had to do was do the above, get crew in (otherwise, why is there need for a pilot visible), and either run the aircraft with the camera crew filming, or keep the aircraft static and run the camera crew around outside (easier, faster).
I don't believe its two separate HS748s either, as quite often there would be some effort in matching the two aircraft footage (most Hollywood movies don't even bother matching planes - look at World War Z), so for simplicity they probably rented one old charter 748 and did a day or less on it.
How was the Burandan Airlines plane made?
Its a paint job on an existing aircraft.
A BBC production, so the people doing it would be an in house production crew.
Just watched that part of the episode, "The Official Visist".
Plenty of aircraft available for a part paint job.
The nose livery is a very common blue flash for the time period, and all you had to do was get a painter up there to paint the name on a blank white spot - notice your view of the aircraft is restricted and limited to not even the whole name.
Heres one that got political:
Typical paint scheme (nose/flash/upper white, lower grey, in this case obviously an Andover of RAFME, circa 1967):