You're stepping into a minefield with this one - there's no easy answer
There's a Black Lion in Black Lion St in 1455 but it closed at some point and re-opened (at a different address)
There was a Cricketers also in BLS that dates from 1547, but it was rebuilt in Victoria's reign
The Druid's Head building dates from the early 16th century but it didn't become a pub until 1830
The Pump House dates from 1776 and was used to pump sea water - it's not clear whether other drinks were available then
You choose the answer that you like
All good enough answers for me along with the K&Q.