Are you saying that you use one needle a day and transfer it from your Levemir pen to your NR pen and then back to Levemir for your evening dose? For some reason I am less comfortable about doing that than using one new needle on my Levemir every 3 or 4 days and another on my Fiasp every 3-4 days. I don't know why I am concerned about swapping a needle back and forth. Perhaps the concern that the 2 insulins may contaminate or impact their performance in some way. Probably negligible risk but just feel less comfortable about it.
I wouldn't say there is a huge saving to the NHS but there is some saving and there is also a slight saving to the environment. A box of needles is probably about £8. If I use 4 needles a week I am going to use just over 200 a year. If I inject a minimum of 5 injections a day (generally I need several more) and use a new needle every time, I am up to 1825 needles a year minimum if I change it every time but more likely over 2000 with corrections etc, so a factor of 10 difference..... plus the extra Sharpsafe boxes plus disposal of them which will all cost someone money be it NHS or council.... I guess it mounts up quite a bit when you actually do the maths. My 1 litre Sharpsafe generally lasts 2-3 years.
Of course you have to also consider the risks of damaging your sites and perhaps even timescales involved in that. ie I was diagnosed late in life and will be unlikely to make it to 100, so not going to have 50 or 60 years injecting and the tiny modern needles are far less damaging than the old reusable needles that many long term diabetics started out using and modern insulins may well also be less damaging. If my fingers cope perfectly well with using the same lancet for a year without harm I am sure my injection sites can cope with reused needles and my experience to date demonstrates that it is OK for me, but I am not advocating others do it.