From the Migration Observatory at Oxford University

In 2013, the UK population was 12.5% foreign-born (up from 7% in 1993) and 7.9% foreign citizens (up from 4% in 1993).
Foreign-born people constituted 37% of Inner London's population in 2013 (the highest share among all regions with comparable data).
India is the most common country of birth among the foreign-born, but Poland tops the list of foreign citizens in the UK.

which sounds as if Britain as a whole has a small immigrant and foreign-nationals population, but London's is much larger. Maybe that distorts how people feel?

Don't imagine that there are no immigrants in Ireland - there are plenty; a few years ago every shop clerk seemed to be Polish, then Chinese. Rumour was that these people were desperate to work, and would work for whatever pay they were offered - way below the legal rates. Now there aren't so many Eastern Europeans and the Chinese have virtually disappeared, but some Pakistanis are appearing. But plenty of Irish people are working in shops and in the other jobs these people were doing, so I suspect (with no evidence but calculation) that the Gardaí may have clamped down on underpayment.