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The delay in the process is purely in the hands of the clearing house because the interbank transfer are claculated over night and sent next day via SWIFT.
I agree with most of what you are saying, however this part I do not. SWIFT is an international system allowing bank to bank transfers, making use of the settlement accounts held at the central banks of the countries from which and to which the payment is being sent.
BACS on the other hand is a domestic payment system where the settlement is carried out by clearing banks on their accounts held at the Bank of England. Banks don't actually send each other money, they just credit or debit their accounts at the BoE.
It is a legacy system, the three day timescale is based on the fact that the banks used to work off magnetic tapes that were processed centrally before computers were networked. Reducing this would require a massive industry-wide initiative, more of this below.
As for CHAPS, this is a completely different system, allowing same-day settlement, where clearing is carried out on a per-transaction basis and not a per-bank basis. The high processing charges mean that the transactions carry relatively high customer fees. CHAPS is typically used for high-value or important payments, where non-repudiation is a key requirement.
In the future, the Faster Payments service is being launched - basically this will allow near-realtime settlement of payments valued under GBP 25,000. The tagline being used is 'Faster than BACS, cheaper than CHAPS'. This is going live between now and next year, different banks have different timescales to accepting these payments.