I don't know what you mean by "HD socket" though, as you said it has "a HD and HDMI input sockets". Or did you just mean that all it has is HDMI?
The only signals that a non-HDMI 360 can put out are analogue and HDMI is digital, so unfortunately it's not as simple as buying a cable. You can buy a product like this: -
http://www.amazon.co.uk/Neet®-Compon.../dp/B002C7CCJ6
That would accept a component input from your 360 and output it via a HDMI cable to your TV, but it's kinda pricey and doesn't include the component and HDMI cables that you would need. I'm not recommending that specific product BTW as I've never used it - it's just an example.
But are you 100% sure that your TV doesn't have other inputs capable of carrying a HD signal? No component? No VGA?