Neither Europe nor the UK are willing to alter their asylum laws enough to disrupt the trade of the people smugglers. The control of borders is illusory if human waves can get onto your shore in boats and the courts strike down most countermeasures, so whoever comes, stays.

Therefore the population boom in Africa is likely to have a massive effect on European demography anyway, unless the Northern African countries, which are culturally different from the rest of Africa and which aren't particularly happy about being used as transit countries for mass migration either, build some kind of barriers across the Sahara.