Just to clarify the above statement. 'In House' means it has to be not only the same bank but the same branch of that bank.
For example, you bank with HSBC NewTown branch and the payee also banks with HSBC NewTown branch. If the payee presents the cheque at that branch it will leave your account overnight - it is what as known as a 'house cheque'. Now even if they bank with HSBC NewTown branch, if they bank that cheque at any other HSBC branch the funds will leave your account at the end of the next working day, ie 24 hours later.
Just to muddy the waters if they bank that cheque at HSBC NewTown branch, even if their account is at another HSBC branch, it will debit your account overnight - it is still considered a house cheque, ie one presented at the issuing branch.
If they bank with any institution other than HSBC, the cheque will leave your account at the end of the next working day.