I hold two Woolwich accounts (which is now part of Barclays) and I transfer money from one account to other on a monthly basis and it always appears in the account virtually immediately. But having said that both accounts are in my name so don't know whether it makes a difference if you are transferring from one to another in a different name.
If the accounts are in different names it will probably appear in the destination account on day 3 - provided it was sent before the cutoff time on day 1. Working days of course.
But it could be quicker as kathyan says, depending on how Barclays do it..
It will go immediately if you have previously transferred money online to that account. However, if this is the first time you have done this to that particular account it will be delayed by 1 day as Barclays will undertake additional security checks.