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The most likely places people from Africa would enter Europe are Spain and Italy. Many of these (I don't know about Spain but it certainly is the case of Italy), although they entered illegally, are allowed to stay and allowed to find work, or are given shelter and a sum of money calculated on a daily basis.
Because they are free to go where they want within the national territory, if they then go a bit further and cross the borders and arrive in Britain, and then ask for asylum, they probably would argue that they did not receive asylum in the first port of call. But if that country, let's say Italy. granted them a temporary or indefinite stay, then in theory they were not allowed to leave that country, as they were being looked after there and provided with money or shelter.
Asylum seekers who do not state the facts on how they got to Europe and how they were received by the authorities of the country on whose shores they landed, and who are then granted asylum, are not respecting the laws on asylum.
It would be useful if the Spannish and Italian authorities made a detailed list of all the people to whom they grant temporary or indefinite stay, because they are obliged to look after them for the period granted. These details should be passed on to all border forces and agencies of other countries in Europe and to Britain.