Can I hire a car without putting down an excess deposit

Excess and deposit are two separate things.

A deposit is compulsory – at Enterprise it's fixed at £200 for most vehicles and £500 for premium and 4x4 vehicles. But don't worry, it is fully refundable provided the vehicle is returned in the same condition. 

Excess protection is optional - you can choose to pay it in order to lower the amount of money you could be liable for in the event of accidental damage or theft.