A couple of years ago i had a customer tell me she sent payment when i didn't think she did. I had to believe her though cos i wasn't 100% sure.
Ever since i ask for cheques to be posted.
I keep a separate spreadsheet called cheques received, with the date, name on cheque, address, cheque number, amount and date banked.
One thing i have noticed since i had cheques posted, is that royal mail have never been more than 4 days delivering from the postmark.
This allows me to privately chuckle when i chase a payment and get told it was posted a couple of weeks ago.