(1) more than just a grain of truth, more like the elephant in the room; net migration into the UK is more than 4 times higher than France, and population density is currently almost 3 times higher, and rising.
Population of 18-65s and percent of total population
2008: 39.2m, 63.4%
2018: 40.9m, 61.6%
2028: 41.3m, 59.3%
2038: 41.3m, 57.2%
Given that tax relies heavily on taxing working people, and the number of working people, and that immigrants tend to be of working age, immigration is essential in stemming the retiree-centric population.
The other alternative would be to swing more of the economy to looking after non-workers (mainly the over 65s), but we won't tax those people despite the massive wealth they have.