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I am interested in the Sony dvp-sr600h, do sony provide hdmi leads with their players
No - you would need to buy a HDMI cable.
The quality and prices of HDMI cables varies widely and are a personal choice. For this reason, I don't think any manufacturers include a HDMI cable with their DVD Players.
If the cable is going to be short, there is no point spending too much - you should get a reasonable one for around £5 from Amazon or Tesco.