Definitely not down to benefits! Illegal immigrants of course get nothing, nada, as they don't exist. Asylum seekers get £42 per week. What do you get in France? £66 temporary waiting allowance while their claim is being processed and income support up to £140 per week (
linky)
So, why do people come to the UK? For the majority, the decision wasn't theirs, third party agents and facilitators sent them this way. A third cited linguistic, family and historical links and the general perception that the UK is a safe place to live. For more information, check out section 6.2 of
this study