Hi gavin121 -
It appears that the HTTP endpoint is operating as expected when accessed directly:
http://ulster.funnelback.co.uk/s/suggest.json?partial_query=pad&collection=funnelback_documentation
Using JSONP might be more appropriate to address the CORS issue:
http://ulster.funnelback.co.uk/s/suggest.json?collection=funnelback_documentation&partial_query=fun&show=10&sort=0&alpha=.5&fmt=json++&callback=jQuery110207145138245942543_1424788157522&_=1424788157523
And finally, if you're wanting the Public UI to serve up responses via HTTPS, you'll need to consider some changes to your Funnelback web server configuration:
http://docs.funnelback.com/configuring_funnelback_s_embedded_web_server.html