We would need a lot more information to give advice. There must have been grounds to arrest you. Giving a 'no comment' interview is not the best idea. I am surprised a solicitor advised it. Do you understand the warning the police gave before they arrested you?
'It may harm your defense if you do not mention now something you later rely on in court'
I may have the wording slightly wrong, but it means that if you do go to court and you put forward an alibi you will be cross examined about why you did not give the alibi when you were first arrested, it makes it look as if you only thought up the alibi after you were arrested.
While you are bailed the police will be gathering evidence to see if there is sufficient to charge you.