Yes, you can shop around for life cover at any time, you do not need to buy from your lender.
Once a life policy is in place that covers the amount and term of the mortgage then the lender must accept this.
Also you do not have to give BOI a quote from the new provider, it's none of their business, more than likely they will match it to try and keep the business on their books - it looks like it's too late for that.
It is advisable to have the new life cover in place before cancelling the old policy - just in case something happens before the new policy issues.