This seems to me to be entirely about the headlines, not about what can / should actually be done. It is a hugely complicated issue and a single, simplistic policy like this isn't going to address it.
My understanding is that immigration involves push factors and pull factors.
The push factors are why people leave their home countries. It can be political / safety (war, famine, environment - earthquake for instance) or economic.
Although we (the UK) can have an effect on these, it is not something that we can change quickly (or on our own). The political / safety factors are why the asylum process was set up in the first place.
The pull factors are, having left their home country, why do they want to come to THIS country, rather than another. Again, this is not generally a single reason.
The first has to do with our country's imperial history. People in many countries have historic links to this country due to the Empire, and there has historically been a subconscious, pervasive idea that England / English culture is something to aspire to, and this has been continued by English being a language that many people speak as their second language. This is not a moral judgement, simply stating the historical context. If someone is restarting their life from scratch they are far more likely to believe they will be successful in a (vaguely) familiar environment where they speak the language already. We cannot change this - it is a historic legacy.
Secondly, there is our internal situation where it is, compared to other countries, much easier for people to work here in the black market. For economic migrant especially, often people from their home country have gone to the UK already and are sending money back. They see this and therefore think that they can earn more here than they could elsewhere.
Add in to that a distinctly lax immigration system (once people are in the country). Our immigration system is woefully underfunded and therefore people are simply let go and can easily disappear. Again - knowledge of this is will be communicated to others. There is a backlog of thousands of asylum claims which need to be dealt with and, even if someone is denied asylum, if their whereabouts are unknown, it is impossible to deport them.
The small boats issue / crack down is a red herring. We need to reduce the pull factors stopping as many people wanting to come here.
To me there are 2 ways of doing this - firstly by ensuring that the immigration system is properly funded so there is the time and capacity to keep track of people who have come into the country. More funding should be provided to ensure that asylum claims are dealt with swiftly and, once the case is decided, to ensure that people can be swiftly removed.
I also think that introducing something like a national ID card would help dramatically - it would provide an easy (hopefully less forgeable) way to people's right to work to be checked and remove a chunk of the black market thereby reducing one of the pull factors.
Sorry for the essay! Even this long, I don't think it covers everything.