I think the solution to both your breathlessness and your relatively 'unhurried' swimming pace is that you are swimming at both too low a stroke count and too low a tempo.
You can correct both pretty easily.
1. Go to the Free Stuff page
on the TI web site and download our Green Zone height-indexed chart of efficient stroke counts. You'll want the one for 25m.
2. Order a Tempo Trainer
If it's available through the UK site, or one of our UK coaches, order it there.
Your 25m Green Zone is between 17 and 21 sol for your height. So 17 is the fewest strokes you should be taking. However it seem as if, this early in your development of TI form, you'd be better off working near the top of the SPL range.
Try this experiment on your next visit to the pool.
: Swim 4 to 8 rounds of 3 x 25. Each round is at 19-20-21 strokes.
Keep repeating this until you can comfortably and accurately make the adjustments in stroke timing that allow you to strike the wall consistently in the target count for that length.
When your stroke is well-calibrated to hit those counts, try the following
Swim 4 to 6 x 50m repeats
Odd: 19+20 SPL
Even: 20+21 SPL
How do your time and sense of ease compare at these stroke counts as at your present stroke count?
If I arrive at 'stroking time' by subtracting 8-10 sec for your initial pushoff and turn (guesstimate) simple math, at 34 strokes and 1m20sec for 50m you're stroking at a tempo of about 2 seconds per stroke (one hand entry to the next).
ANYONE--even the most skilled and experienced of those on this Forum would be slow and feeling short of air at a tempo that slow.
That's where the Tempo Trainer comes in. Once you have it, choose Mode 1 and set tempo initially at 1.5 sec. At that tempo, and synchronizing first hand entry following pushoff to 4th beep, find out how many strokes you take. If it's 21 or fewer, then begin pushing left button, to increase tempo. Just .01 sec every 25 or 50 (as 2 x 25 with some rest between) m. Test how many tempo changes you can hold that stroke count.
Please post the results of your experiments, and what you discover, here.