Thanks for the extra info.
I have never gambled on line with or without bitcoin, nor even used BTC to buy anything. I definitely didn't spend the coin. If the coin has been spent then it looks like I've been scammed. But if I've been scammed it is odd that they didn't move the coin immediately in September. Perhaps they were waiting for me to put more into the wallet.
I have a brief note that I wrote for myself when I made the payments into the missing wallet, along with some login information, and I think this must be the location of the wallet, though it wasn't the clearest of notes and I wasn't sure.
The web address that I noted down is bitcoin-central.net, and I also noted one of the addresses of the missing wallet :- 13J4Ly36hyVDyWT37fqJUm5vRCyiqengQ1.
I haven't found a way to contact bitcoin-central.net. Their site now has no contact info and no login page. Whois.com shows an entry but the contact email address bounces back.
I googled bitcoin-central a few months ago and found a link between them and paymium.com. The login details that I had noted for bitcoin-central.net enabled me to log in to paymium.com, and it even showed me my bank details. However, paymium.com don't admit any connection to bitcoin-central.net or the possibly unrelated bitcoin-central.com, and I get the feeling they are not wanting to answer my questions properly. I have uploaded our correspondence to my own website as a plain text file, including a question (a repeat of a previous question) that I added just now.
https://softbyte.co.uk/_dwnload/paymium.txt