I think that anybody and everybody with half a brain cell had already picked up that Cameron's pledge to reduce immigration to the tens of thousands was just pure tosh - it did not happen when he was PM and in fact it only increased.
What is needed - and leave voters are generally, IMO, able to fully understand this, is effective policies that can apply to all migration - either from the EU or the ROW - that introduce controls on immigration.
Controls might be in such areas as requiring there to be a job offer to come to, or limit the amount of time a visa runs for, limit access to benefits etc. There are models around the world where be can draw up effective policies from to meet our needs.
Cameron's government utterly failed in their pledge - part of this was down to not being allowed to bring forward policies for control of all migration due to the freedom of movement principle and part of it was down the government incompetence.
If we end up leaving then we will be able to introduce controls
'Taking back control' in all key areas, especially borders, laws and money is what it is about. Immigration was a focal point due to the perception of the impact on all key services and infrastructure. It is likely that this can be diffused if it can be clearly evidenced that, whatever the volume, it is under control and net-beneficial.
Now I will agree that in the campaigning lots may have been exaggerated on both sides - but now we are past 2015/16 and in to the preparations for reality, the target should be to match immigration to the UK's service and economic needs.
I would be surprised if May makes any new forecasts, which would be an hostage to fortune, between now and the 2020 GE. She will want to see:
a) if we have actually left the EU
b) what Amber Rudd brings forward as the immigration model and policies
c) what the projections are for what the needs of key services and the economy are
She will, if she is sensible, want to make achieving 'required and controlled migration' her policy and avoid arbitrary numbers. If she does that then it will be self-evident that whatever the immigration flow develops into is beneficial to our nation.
I accept that Remainers can now position this as 'rowing back', - so be it, enjoy the victory. Double up on it and point out that if reality on the numbers of future immigrants coming to the UK had been fully known then it may have affected the result - all though that is not at all certain. That is still living in the 2015/16 world. I and I suspect many leave voters have moved on, so will be open to evidence that migration is becoming under control to achieve the level being 'net-beneficial'.
For me it is just devising the required strategic and long-term policies with the right sense of control and pragmatism. This is what we need in the future as we secure our own controls - for me that is what the outcome/legacy of the referendum should be all about.