Does this mean that double entry book-keeping is practically a blockchain, with each block being a transaction?
Not exactly. In double entry book-keeping, every institution keep its own accounts that reflects the truth. This means there are 2 version of truth and there is reconciliation between these 2 truths to agree on actual truth.
In blockchain, there is single copy of truth that every one can refer to.
For example Bank A opens a Current/Checking account with Bank B. This account that is held in Bank B's book is called VOSTRO [Say number 123] and Bank A maintains a version of this account in its book. This is called NOSTRO [say numbered 789]. Every time Bank A makes a payment / or receives credits on Bank B account, it reflects this in its book in NOSTRO account 789. Like wise Bank A would keep a record of this on Account 123.
Ideally both these entries should match; in reality there are some discrepancies. These are hence reconciled every day. Sometimes its due to date the entries are off; sometimes the entries are missing / incorrect due to various reasons.
In blockchain, the idea is there is one account, say ABC. Whatever is in this account is truth and Bank A, and Bank B [or any related parties] can look at it. The recon is much easier by Bank A and Bank B; as they get to see complete set of same transactions that have hit the blockchain.