The truth is that couples need to have on average two to three children. No immigration is then required. Some countries have accepted that low birth rates will diminish their populations, but they don't want mass migration. This applies to Japan where there has been a public debate.
Three will then lead to a slight increase in the population for each generation, bearing in mind that 10% of couples have fertility problems and another 10% have no maternal instincts which should be respected and there is also an attrition rate.
We need to have a slightly increasing population otherwise our welfare scheme will collapse, where it has the structure of a Ponzi scheme. It has no money, so the money from new entrants and current contributors, have to payout all bills to current, past and non contributors. While new entrants and current contributors equals or exceeds payouts is it viable, currently it is not, hence the UK deficit. If something isn't sustainable it won't, hence at some point it will collapse. Blame Lloyd-George and Attlee for its construction.