Les, my source for that was a Time-Life publication, The Fighting Sail. They didn't worry about the niceties of the vice- or rear- admiral. The Oxford Companion To Ships And The Sea reports that he was promoted to REAR admiral of the Blue six days later by seniority. He was also given the honorary rank of colonel of the marines because the boarding party he was leading was made up largely of marines.

The full name of the bridge according to the Oxford Companion is Nelson's Patent Bridge For Boarding First Rates.