In short, yes. Evidence is rarely presented at the point of arrest.
If you've ever seen an arrest take place, the UK Police Officer will state "I'm arresting you on suspicion of..." or "I have reason to believe..."
It is then up to the arresting officer to present the evidence to the custody officer to justify the arrest and continued detention or release on Police bail (or de-arrest and release).
There are very strict rules and penalties for officers who abuse their power of arrest, but legally they can arrest anyone at any time.