The money saved by cutting IVF does not 'go back into the NHS'.
Commissioning bodies are required to make savings every year. As in reduce how much money they spend. If a local body cuts IVF it is a cut, not a transfer of funds.
It does of course mean that there isn't a cut, or as big a cut, in another service.
IVF isn't overall a 'big ticket' item and does not account for a huge amount of money, but it's the sort of treatment that can be considered for cutting as, basically, it's not treating a life-threatening disease. This is why prescriptions for gluten-free food are going, area by area (mind you, nobody should get pizza and cake on the NHS). This is why some areas no longer prescribe any OTC anti-histamines. To save money. Together these items add up to maybe enough to meet the government-imposed targets for savings.
But of course the crisis is now so bad that even cancer operations have been cancelled in the last month due to pressures on beds. This is happening across the country.
We need our national politicians to sit around a table and have an adult conversation about how much we should spend on health and social care, and what people can expect from these services. If we are going to strip back the NHS to a basics service, this should be by a decision and consent not death by a thousand cuts which is what is happening at the moment.