What sort of Post Office Account are you talking about?
If it's a Post Office card account (purple card, used for benefits and pensions) then the answer is no. There is no way you personally can deposit money into the account - only the DWP etc can do that.
Further to the above answer if it is a Post Office savings account then just write out a cheque payable to yourself and take it into your nearest Post Office with your savings account book.