Have you tried speaking to your local council Park Department or the forestry commission. The New Forrest is not far from you.
As I am in London there is a shortage of forests around but most councils have parks and trees that need to be cut down for various reasons. I sent an email to my local council and they said they could possibly supply me with some logs. I have yet to see what they can come up with as I managed to acquire a few logs from a local tree surgeon the next day but its worth a try.
The only downside is it will be green timber and need seasoning or turning wet and leaving to dry.