I hear you and numbers when you just say numbers sound scary as it is. 1m in 3 years becomes 2m in 6.
However given the fact that immigrants are essential to services like healthcare and building infrastructure as well as the many jobs that need to be done add on the fact that we have and will have a significantly older population, just explain how it is unsustainable, rather than simply saying numbers or saying it will affect services without considering the essential side they bring.
Conversely, though, a lot of those immigrants are working for those national services. NHS being the prime example.
See this is why the immigration conversation is almost taboo, because people assume when you bring it up that you're anti-immigration (not saying either of you assumed that btw). For me being anti-immigration would be impossible since I'm an Irishman living in Australia, who is about to move the UK and hopefully on to the US a couple of years after that.
Immigration is essential, especially when it comes to diversification of culture and ideas. I am also an advocate of refugee intake.
However, migration has to be managed because there are major issues to not managing it properly. That is on both sides of the coin too, for the country receiving immigrants unmanaged and for the immigrants themselves. There are many 'invisible' immigrants in the US, UK, Europe and Australia. Illegal immigrants being exploited and unable to avail of essential services like healthcare and government benefits, unable to go to the police when they are attacked, even raped in some cases.
Managing immigration properly allows for key services to be implemented to ensure that the experience of the immigrants is optimised. And you can't solve the problems of the world in one day, opening borders would simply move the issues people are fleeing from to another place. The execution of immigration policy has to be strategic and considered.
Probably one of the major problems in Britain with regard to immigration and national services and the influence on Joe Public and the leave campaign is that not all issue faced in Britain are related to immigration. There has been a sustained period of austerity that has hit national services. Average people see the waiting queues etc. and hear the immigration debates that are largely over-stated and blame immigrants for problems probably caused more by bad planning and a lack of investment by the government.
All that doesn't mean that a proper managed approach to immigration isn't something that should be applied. Especially in years of austerity... Imagine the government has been cutting funding whilst at the very same time net migration has been steadily increasing. That's how it is unsustainable.