it depends on 2 things, one is the time of day you send in the appeal, the 2nd is how much of the information you know.
If you will in all the info correctly and theres no doubt that the account belong to you then you will get it back in less that 1 hour. Because these can be processed by the computer, if most the info is wrong then the appeal will be passed on to an agent this will not normally take 2-4hours. As they all work in the UK the appeal will be answered faster if they are sent during the day. because if its an night they may not get to it and it ill be left till the next day.