First of all, anti-immigration proponents like yourself are already heard, in fact i would suggest they are one of the more vocal parts of the population. The tabloid newspapers are filled with them, the BNP support this position and indeed this QnA forum has many questions from people who agree with your opinion, right or wrong.
Asylum seekers get 70% of the benefit available to a UK citizen, they don’t get huge benefits, that is a MYTH. Asylum seekers are refugees who do not have their status confirmed, they are not allowed to work (unless they have been here over a year and the Home Office still has not approved their case or deported them), the money they get comes from central government not local sources so it doesn’t effect the local economies, and they made up (in 2003) 0.5% of benefits claimants, thats about 80,000 out of 15million.. Even if that has gone up by 500% since then its still a tiny amount compared to the lazy UK citizens who make claims (figures do not include pensioners).
Illegal immigrants are a different matter, do not confuse asylum seekers with illegal immigrants they are not the same. Illegal immigrants cannot claim any benefits without committing fraud, they are the same as UK citizens who claim benefits and work, they are criminals.
Being anti-immigration without actually thinking about it is the first step to ultra-nationalism. Immigrants are important to the UK as they bring new ideas, culture, money, connections for business export, labour for jobs which are difficult to fill with UK citizens (farm, slaughter, dirty, unskilled etc) and with our rising aging population, slipping birthrate and economy teetering on the edge (with regards to lending) we need the constant renewal of immigrants to ensure a healthy future for the country.
Now I agree there need to be limits, however just saying “i am atn-immigration” is like saying ” I am anti-cars because people die in accidents”, we still need cars we just need to make them and the roads safer through better control.

Not anti-asylum but anti-immigrant?
Then Britain will have to quit the EU because immigration is 90% EU/EEA/Swiss nationals who cannot be kept out because of the European Communities Act 1972. For the rest, it’s mostly family reunification, and to keep out spouses and fiancé(e)s of British nationals you’d have to denounce the European Convention on Human Rights and Fundamental Freedoms and abrogate the Human Rights Act 1998 as well.
Beyond that, most immigration is highly skilled or under bilateral commercial treaties, so you’d have to denouce the treaties of friendship, commerce and navigation with the USA and other countries.
And for the rest you’d have to abolish the Commonwealth and stop giving any rights to grandchildren of British-born emigrants.
The last, tiny, category consists of a few hundred people a year who are here illegally and manage to stay out of sight and out of trouble for fourteen (14) years; or legally (as a student, etc.) for ten (10) years. And an even tinier group, servants brought to Britain who have worked for British or non-British families, mostly either wealthy or diplomatic, for two years and then come with them here and worked for them for 4 years here.
There are a few other categories that involve another few hundreds: journalists and ministers of religion. I suppose you could ban them from coming, but then there would be retaliation and the BBC and the Church of England might have something to say.
Then you could abolish immigration. But you’d probably also have abolished a lot of jobs, and an enormous amount of investment.

illegal immigration is illegal immigration whether you are in the UK or the US. Ever notice that people don’t illegally immigrate to Syria? Create a 360 Page and write about it, there are some good ones out there you can follow as an example.