The short and simplistic answer is your organisation could be liable in theory, but you can protect yourself by making it a condition of the donation that liability passes to the donee organisation.
A couple of other points to consider:
Are you a business end user of computer products, or a manufacturer ? Was the equipment brought before 13 August 2005 ?
If you are an end user, you have primary responsibility for the collection, treatment and recycling of computer units purchased prior to 13 August 2005.
Where equipment is purchased post 13 August, primary responsibility for such recycling passes to the manufacturer. However, the UK implementation of the law has a loophole which allows manufacturers to pass this burden onto the people who buy their products under their standard terms and conditions. So even after 13 August 2005, you will need to check whether the contract for the equipment you have bought passes the liabilities back to your organisation.
To answer your actual question, most of the major organisations who accept donated computers (like Computer Aid) take on (as a matter of contract) all future legal liabilities for the items when they are handed over, so you wouldn't need to be worried about retrospective liability.
It will be more of an issue for you if you donate to smaller, local groups. However, again, you could agree as a condition of the donation that they will be responsible for all legal liabilities in connection with the equipment in future.