On a dual carriageway when the vehicle you want to move in front of looks far away in your door mirror are you just judging their distance or judging their speed relative to yours too? Are they gaining on you? You need to be going as fast or faster than them before you start your lane change and keep your speed up until you arrive ahead of them without slowing them down.
The most common mistake I see learners make on the dual carriageway when they want to overtake is slowing down to look in the mirrors, then the gap they wanted to move into starts getting smaller and smaller, so keep your speed up until you’ve had a look, you may need to speed up, maintain speed or slow down, but you need to hold your speed and take that look first before you make a decision.
Here’s a nice method to judge that: If you can see the vehicle you want to move in front of 100% in the interior mirror (not the door mirror) and they’re staying there then you have time to move lane in front of them without slowing them down. Don’t just rely on one look, keep checking before you start changing lane and as you’re making your move. If the vehicle starts to disappear out of the side of the mirror they’re getting to close, so you either need to speed up until you can see all of them again, or if you can’t because of the speed of the vehicle in front of you or the speed limit then if there’s no-one behind them ease of the gas a bit, let them pass and then slide in behind them. If there’s a few other vehicles behind them then indicate to see if they’ll let you in, you want to see them very obviously backing off for you, or maybe a wave or a flash. If you’re pretty sure they’re letting you in then speed up a little and as you start moving sideways keep watching them to ensure you’ve read their intentions correctly.
On a single carriageway road be sure that you can see the whole distance that it will take you to be on the wrong side of the road while you overtake. Be patient and hang back regularly checking mirrors in case someone behind you tries to overtake you, then when you see your chance go for it wide and fast (within the speed limit) so you can get back to the left as soon as possible, but before you do check the left mirror to make sure you’re well clear of whatever you’ve just overtaken. Avoid overtaking on right hand bends as they are usually really bad for visibility (unless there’s a field on your right). Also look out for side roads on your right with anyone waiting to turn left, they may be busy looking the other way for a gap and when they pull out they won’t expect you on the wrong side of the road heading straight at them!