Please define what you mean by 'screensaver'.
Please define what you mean by 'flashed up'.
And do you believe your neighbour? How does he/she know what your 'screensaver' looks like?
Things to check are:
1. Make certain that your SSID names in your routers are clearly different.
2. Make sure your router uses a different channel to your neighbour (use a site survey tool to find out what channels are in use).
3. Don't use the default IP address on 192.168.1.0 in your router's DHCP server. Use something like 192.168.156.0 instead so there is no chance of confusion.
The photo of my dog which I have set up to show on start up.
Seems he had a window appear "mirror screensaver?" which he cancelled several times and then opened out of curiosity.
He recognised my dog! .
Not happened before.
Thanks for suggestions