If you already have a composite / AV out lead for your 360, all you need to connect that directly to the TV is one of these:-
https://www.amazon.co.uk/dp/B0014HB4YO
Available from other suppliers, that was the first one I found.
Converting from HDMI to SCART is certainly a level of complication you don't need but either way, you are 'downscaling' to SD by not directly using either the HDMI or VGA output capability of the 360 so you won't get very good picture quality.