Our immigration policies have also lacked discernment. Whilst in principle it's fine to have some unskilled immigrants and assume that society will absorb them we have had large numbers of unskilled and low wage immigrants - many of whom have made no attempt to adapt to UK society but for whom we as a nation have adapted to.
Whilst the debate about the nature of Islam is complex it often feels like whilst it's okay to joke about Christianity and other religions it is not tolerated by Muslims and that religion has to have special treatment. We have also received many immigrants from Pakistan and Afghanistan who follow a very hard-line form of Islam - who whilst we compromise they often will not do so and many of whom hold views about women and gays that are contrary to ones we as a western liberal society try to teach. Its probably quite unhelpful that the dominant form of Islam in the UK is one of the least tolerant and most hard line interpretations of that faith. Consequently we have situations where circa 45% of working age Muslim women in the UK are not in paid work.
The UK tax system levies no income tax on income up to circa 12k and then 20% tax up to the next 40k (50k ish in total). So someone on 30k pays circa 4k in tax and NIC, whilst the government pays out 17k per head of population for services. This means migrants are tax negative for the UK.
On top of this the amount of houses per head and infrastructure per head of population is less. House building is much lower than required. We haven't built many new roads or railways for instance but have to fit many more people on to those roads and into those parking spots.
Whilst immigrants may have taken jobs British people don't want to have its a lazy justification for high levels immigration because ultimately as a nations we have many unemployed who should be working and we should also train enough people for key industries and pay them appropriately.
Consider how much lower UK house prices would be with 15m fewer people? How much lighter traffic would be on the road and how easy it would be to park in towns and cities? Also how much higher NHS, social services and education funding per head of population would be due to fewer tax negative migrants. Its easy to understand why people feel like the level of immigration has been too high, lacked discernment and not benefited existing citizens.