You are mixing things up and getting confused.
Of course there are crimes in the EU, nobody as said otherwise and nothing is 100% foolproof remember.
BUT, they are not all committed by people who already have a record as already mentioned and without a criminal record how do you predict?
We are no longer privy to those who do actually have a record as found out by another EU country, or who are considered a threat, whereas the ones in the EU who share information, fingerprints and track illegal immigrants etc do. I presume those ones are then not granted asylum and are removed quite fast and if a person tries again in the EU, the information is there. The information as far as I am aware is digital and quick.
We now have to rely on finding out each and every asylum seeker from scratch, we only have slow and not very good interpol really and our own methods. So, even if they had already been refused in another country because of criminal background (or whatever reason they are failed asylum seekers), we don't know. Adding to the backlog of a year or so waiting, allowing people to roam our streets freely while they wait and of course, the cost of hotels etc with that backlog keeps mounting.
Losing access to this information of Eurodac and SIS II because of brexit has hurt us, not just because of immigrants but many other types of criminals. If you don't believe me, please go read. It's one of the things Starmer tried very much to get access to again in the EU with good reason, but they refused. It would've helped massively with the backlog of cases that they inherited. Sharing information on criminals, not just immigration related too has stopped for the most part, leaving the UK more vulnerable too.