Nitrite can rise a long way above the limit of the test kit. When that happens, it can be disheartening waiting for it to fall low enough to be back in the range of the kit. A good way to tell whether it's peaked and beginning to drop back is to start testing for nitrate. If the nitrate level begins to rise, then even if you can't see a drop on the nitrite test you can be sure that it is falling and you're on the home straight.
Ah right! I see. Well last night the nitrates were at 40ppm. Tonight I checked ammonia and nitrites and the ammonia was all gone so I dosed to 3ppm. The nitrites increased to around 1.5ppm - haven't checked nitrates today but they seem to be shooting up without too much nitrites being present.
The tank seems to be able to process 3-4ppm ammonia every 24 hours now but nitrites are still off the chart. Nitrates are the same. Should I be doing a water change to bring the nitrates down or do they not affect the cycle enough to worry?
Very glad to hear it's going well at last. High nitrates can slow down a cycle, but only because when nitrate is very high there is usually a lowering of kH and pH accompanying that, which are the real culprits. In your case, your tap water is low in carbonates which seem to be rising in the tank for some reason. I would check kH and if it's down to 1 or under do a 50% water change and add a level teaspoon of bicarbonate of soda to immediately raise kH.
Hopefully, you're not going to have to wait much longer now and will soon be able to actually get some fish
Quick update and seeking advice. So I still have off the scale nitrites after them appearing almost 3 weeks ago now. I measured the kH which is at 3 degrees at the moment. The nitrates are also off the scale at the moment. I also measured the pH as I hadn't done that in a while. It is sitting at 8.4 but I suppose this is to be expected with these extremes of nitrogen based compounds in the tank? Is there something I could be doing to help speed this up?
After this long a 50%water change may help. use water at approximately the same temperature as the tank (test by dipping your hand in) and make sure to dechlorinate it before it goes in. I would imagine nitrite is falling, just still above the range of the test kit. I would expect to see it come down pretty soon now.