No. Live fish cannot be sent using regular mail services like Royal Mail in the UK, because it has not been authorised by the Animal and Plant Health Agency to carry live animals, required by the Welfare in Animals Transport Order which covers Great Britain.
Royal Mail also makes clear in its list of prohibited items that it will not handle live animals.
If you offer collection only, then the purchaser can transport their new fish home in their car without needing an authorisation to carry live animals. However, even as a private seller, if you choose to send fish to their new owner you must use an authorised courier, such as APC or DX Courier. You must also pack the fish properly.
