The course of events would be:
1. Rahman receives £500,000. 2. Rahman withdraws £60,000. 3. Barclays considers this suspicious, so suspends Rahman's account for seven days pending further investigation. 4. Rahman presents his evidence of where he got the money in the hope of his account being released in under seven days. 5. Whether Barclays accepts Rahman's evidence or not, they fail to gather a criminal standard of evidence against Rahman within seven days, so release his account anyway, since to keep his account suspended further would be illegal.
If Barclays does not do 5, then sure, Rahman will end up in the same situation now. He'll spend the same amount of time as he did already in getting it resolved. However, when he does get it resolved, Barclays' settlement will include consequential damages for the house he failed to purchase because of Barclays' illegal suspension of his account.
As it stands, since keeping Rahman's account suspended was not illegal for Barclays, they don't really owe him anything, so his settlement is much smaller and he is still out of pocket because his house purchase failed through as a consequence.
> Imagine the delay and cost if this had been handled in court.
The court would have nothing to handle, so Rahman would incur no delay or cost.