Any one person's fertility, in the UK especially, is going to have no meaningful impact on population growth. In fact -- ironically -- fertility treatment is probably linked to a more controlled population, albeit indirectly (the logic being that having advanced fertility treatment will come hand-in-hand with better overall healthcare, including contraception).
So it's a stupid point. I can happily concede that fertility treatment as a whole shouldn't be on the NHS, all the same, but not because of some trumped-up fears that it will lead to a dangerous population explosion.