There are some excellent, intelligent and, indeed, persuasive points being made here (plus a thanks to Sucky for his particular input) ...
My thoughts - for what they are worth:
Immigration - the country is certainly in crisis on this - not caused by this Government - but it is their problem to deal with. Need to differentiate between Legal and Illegal immigration and also deal with Asylum seekers. Brexit has certainly exacerbated the 'problem', because large numbers of itinerant / annual migrant workers from Europe ceased coming as a result. Those job vacancies are tending to be filled by immigrants from the third world, in large part because we have a generation(s) of 'Brits' who are content to live off the efforts of others and not contribute to society themselves. As part of an overall initiative we need to make working (minimum wage) way more attractive then living off benefits - for those able, but unwilling, to work.
Asylum - all asylum seekers need housing in secure holding facilities with no access to general British society (only possible exception would be educational for kids) until a decision is made on their application - if successful, they become British citizens, if not, they are deported. Those without papers held until their identity can be verified - the onus of proof on them.
Integration - for me this is (or has) become a major concern for most Brits - IMHO it is not healthy for society as a whole to have enclaves that resist integration into (an appreciation of) our broader 'British' society and its traditions and values. I would therefore favour a initiative similar to Australia - new arrivals (successful) need to swear to uphold the constitution and values of the country (which they have chosen to come to) and must seek to achieve a basic understanding of, and ability to communicate in, the English language. There should also be a compulsory induction during which it is made clear that this country is built upon principles of equal rights for all sexes, orientations, religions and races - and that there are no 'local community' exceptions to that base principle. Anybody objecting to those conditions should be 'helped' to find an alternative country, more in line with their preferences / principles.
Intolerance - in whatever shape or form, and towards each and every community, race, religion, orientation etc needs to be seen to have equal, serious, measured punishment under the law.
That's All Folks ... and just my view, as always.