It's a more complex issue than Morrissey describes for me.
Immigrants often set up their own communities. This means that they aren't diluting British identity, just adding their own. I guess the bigger issue is, does multi-culturalism work or would any immigrant population be more successful by being inter-twined with the resident population?
Mass immigration has dual purpose of keeping wages low and giving the likes of the BNP and UKIP the chance to whip up misplaced hate from the UK population blaming immigrants themselves for their woes, either financial or perceived cultural.
Mass immigration provides a very successful divide and rule tactic. Everybody points their fingers at foreigners - this is whipped up by politicians who like to use immigration as the cause of the country's problems. They're scrounging (most are no doubt working their arses' off to better their lives), they don't learn English (most do), etc.
It suits a government (whichever is in power) to promote immigration. Why? Each election is paid for by donations from people who expect to have their interests met on the return of that government. While that government is in power these same people will be putting pressure on that government to insure that their interests are met. Sometimes people in the government are part of these pressure groups, surely a conflict of interest but we're living in corrupt times. I digress...
The needs of a greedy and corrupt establishment (The government/corporations/media/etc) are well served having a population that attacks each other rather than hold them accountable for how the country is run.
My own opinion is that most people who move countries do so because they want to improve their lives. That said, I do think any population is better integrated rather than celebrating multi-culturalism. Our biggest problem is the way how our political parties are funded and how much power very few people hold over us. Immigration is just a very convenient distraction.
One other point, our identity has been heavily formed by immigrants so that's that really.