Having a "correct" technique to make your instructor or examiner happy is one thing, but the most important thing is that you have a technique that you can rely on to keep you safe when bad stuff is happening and you're under the pump. Diversions in the real world generally don't happen in perfect conditions, with plenty of time to orbit or faff around with your head inside the cockpit while you plot a nice neat course on your map, fill out a leg on your flight log and all the rest of it. More likely, it will happen when you are caught by unexpected bad weather, a sick passenger, an electrical failure, caught down low under a cloud deck in poor visibility, or some other pressing issue that requires you to direct your attention outside. Often, in these situations, time is of the essense. So you need to be able to just decide where you want to go, and get going.
With practice, it is possible to estimate angles surprisingly accurately without the use of a protractor or a drawn line. If you have plenty of time with which to plot it all out, then by all means do so. But when you're under the pump, with last light looming, the fuel gauges flickering towards empty, or dodging clouds in poor visibility with the ALT FAIL light on or the oil pressure gauge flickering, it is far more useful to be able to glance at your map and go "that looks like the place I want to get to is just south of west from here.....let's say roughly 260 degrees about eighty miles", point the nose in that direction, and get going. Refine it as you go, by all means, but get the aircraft heading roughly in the right direction as a priority. Unless of course, you don't know where you are......in which case you are not performing a diversion, you are performing a "lost procedure".
Accuracy is important and you are right to try and get your ETAs as accurate as you can. But always, always retain the "big picture" in your mind. You are far better off to always know roughly where you are, than to spend so much time bogged in the paperwork trying to know "exactly" where you are that you get completely befuddled. Sometimes it really is as simple as just making an educated guess at a heading and time interval, pointing it in that direction, and then just concentrate on looking outside and getting yourself oriented.
Bear in mind that my experience is based on flying cross country in parts of the world with lots more open space and featureless terrain than you have in the UK. You don't want to take this too literally and get so slack with your planning that you risk busting airspace or getting lost. But having found myself needing to DR my way home over several hundred miles of featureless country more than once, I have generally found that the simpler you keep it, the better the outcome. Pre-flight planning is extremely important, but when you're in the air, keep it simple.
As an exercise, perhaps try pulling out a map at home, pick out a few airports or major landmarks, and just "guess" the bearing and distance between them. Write your guesses down, then come back later and measure them with a protractor and ruler. With some practice, you may be surprised at how good you can get at it. Even if you still plot it all out during your skills test, knowing that you are capable of finding your way about without doing that if necessary will boost your confidence and make you much quicker and more efficient in your planning.
(P.S. Are you flying something like a C150? If so, then you are doing around 1.5 miles per minute, or 2 miles per minute in something faster, like an archer. If you're in a C210 or Bonanza, then 2.5 miles per minute, or three miles per minute in a 310 or Baron. You can estimate your ETA just by dividing your "rough" distance by those numbers and unless it is blowing a howling gale, you won't be far wrong. Even if there is some wind, it should still be close enough to get your ETA accurate within your 3 minute margin without needing to pull out a calculator or whizz wheel. The faster the aeroplane, the more accurate this method is. Yes, it's a bit rough, but it works.)