Mortgage Inversion Complete, What Next?

I completed the transfer of money into our brokerage accounts from the "mortgage inversion".  That completes a major step in our financial restructuring since the inheritance. We've completed the first two steps on this list. I am thinking of refinancing our mortgage to get a lower interest rate now I don't care about having an offset account with my main bank. But how to go about this? Should I go to a mortgage broker or just contact a bank, like HSBC, who are offering a low rate?