Much as you may like to as the UK is signatory to a number of international conventions concerning people claiming asylum they cannot just be deported once they have claimed asylum. There is a process. The Home Office has to look seriously at their claim and I can tell you the following nationals stand a high probability of being granted asylum: Syrians, because their country is a war zone, likewise Sudan. Eritrea because it is an extremely repressive dictatorship with widespread documented human rights abuses. Iran if the person claims and can reasonably prove to be a christian or if they are gay. During the course of an asylum claim the person claiming asylum has an initial screening interview and then, eventually a substantive interview which goes into detail as to why they should be granted leave to remain. Often because the person has no documentation NOT because they have been told to destroy it as claimed by that Migration Watch website and the Telegraph but because they have had it taken from them at some point by traffickers/smugglers OR they never had any in the first place, during the course of the main interview the Home Office will seek to ascertain if the person is, indeed where they claim to be from. They will ask the national currency of their country of origin, they will ask for well-known landmarks in the areas of the country they claim to be from. I know this for a fact because I have attended a number of these interviews.
Your bias is obvious, you want all these people gone by whatever means. But ask yourself this: why would someone make what is very often an extremely dangerous journey of thousands of miles to claim asylum in the UK? If they have traveled through Libya to get here I can 99% guarantee that they will have suffered exploitation and abuse; I have heard horror stories that would make your skin crawl. People are then subsequently traumatised and often have PTSD. People travel here to claim asylum mostly because they are desperate and they feel that they have absolutely no choice. Do not be so quick to judge. Also take this discussion to one of the relevant threads which have already been pointed out to you.