I'd say between five to ten years duration from arrival/registry to full citizenship, no "citizenship test" farce as we have now, and would define "offending" as being found guilty of an imprisonable offence, with a presumption that you would be removed if you breached that condition of non-offending. I'd also get rid of the "You cannot work until you get leave to remain... rubbish". Immigrant workers would have exactly the same rights - minimum wage, union representation etc - as everyone else.
The prospective applicant would first have to contact a UK embassy or consulate, if not in their own country then at the first available one. They could then get registered onto the system and come over here legally and without being forced into the hands of people smuggling gangs, who of course are behind so many of the evils that immigrants coming to this country face.
Immigration staff would be expected to grant entry, unless there were grounds not to (ie: previous failed application (identifiable by fingerprints), illegal entry to the UK - in this system there would be no need to sneak in because they would let you in or possibly because of criminal behaviour elsewhere, though this would depend on the circumstances). They could then focus their energies on identifying and removing the people who should not be here.