I have an array of receiver machines setup for dual-booting Ubuntu and Windows. When the receivers are booted into Windows I can ping them over wired connections (192.168.1.X). Having copied the exact same network adapter settings into my Ubuntu partition, I cannot seem to ping the receiver machines anymore.

For clarification, I am using the same hardware setup (so ethernet cable is plugged in the same port), adapter setup is the same (e.g: IP is 192.168.1.82 on Win10 partition and 192.168.1.82 on Ubuntu), mask is set to 255.255.255.1 (same as Win) and gateway set to 192.168.1.1.

After googling the issue there appeared to be some hints that it might be a firewall issue and to try SSH/something that uses a different port. Having tried this, it didn't allow me to connect via SSH either.

The sending machine is definitely configured correctly as this can ping any of the machines booted into Windows. The receiving machines are also not connected to external networking.
I haven't used the machines for a while but I seem to recollect them being able to communicate previously.

Has anyone got any suggestions as to how I might go about getting them communicating or where the issue may be?

I assume what you posted is a typo error but the just in case it isn't I am assuming the netmask is actually 255.255.255.0. As far as I know Ubuntu does not block ICMP messages so ping should work regardless. Are your "receiver" systems headless? Can you ping from them to the sending machines?

You might try traceroute to see exactly where the ping is breaking down.