I used to have problems too.
Use fresh eggs, don’t add salt to the water. Add a drop of vinegar. Only use 5-6cm or water. Boil it but turn the heat down so it’s not bubbling when you add the egg.
I crack the egg into a small plastic soup ladle and then before I carefully slide it in the water I swirl the water. Slide the egg gently into the whirlpool at the centre. Water must be hot, but not bubbling as that will break up the white part.
You can also buy an egg poacher which will do four at once. It’s the cheats way but gives perfect results every time. They are not expensive. See image. Google egg poacher
Thanks for the suggestions, I will certainly look for an egg poacher. I didn't know they existed.
I have one and they work really well. I use it if I need more than two eggs at a time. I read somewhere you can also microwave poach eggs in a coffee cup or glass with a little water. Might be worth some research for you.