Asylum papers aren't citizenship, and do not give the rights a EU citizen has (I believe typically they don't allow to leave the country), so the UK can freely choose if it wants to let them in or not.
> I believe typically they don't allow to leave the country
They do:
> You can travel to the so-called Schengen states (Belgium, Germany, Denmark, Estonia, Finland, France, Greece, Ireland, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Austria, Poland, Portugal, Romania , Sweden, Switzerland, Slovakia, Slovenia, Spain, Czech Republic, Hungary) without a visa, if you do not stay longer than three months and you do not work there. [0]
In the EU that's a moot point anyway as I haven't seen any border control in years. So at least travel-wise they're quite free to move.
