The postcode/address check might be enough to make you decide whether to contact the estate agent at all, even if it isn't accurate for a specific house, and doesn't distinguish between whether FTTC is planned or FTTC is already live (same for FTTP, which is restricted to parts of the Bradwell Abbey exchange).
After that, ask the estate agent (or letting agent) for details.
They can certainly decide whether to be helpful, but I guess if you specify to the agent before you mention any single property, then they know it is a serious criteria, and you know whether to bother dealing with them again.
If they choose to be helpful, they can ask their client for existing details.
They probably know the client's phone number, and may also be persuaded to give you the results of the DSL check (with number redacted).
Another way would be to get the postcode (easy once you know the address), and use either Google or 192.com, and search for the phone numbers in that postcode (eg include the dialling code in the search). Or find names in the postcode, then use BT.com's directory search to get phone numbers. Or just guess names (eg common surnames like Smith, Jones etc).
A while back, I used the Cabinet/Postcode Map at Timico's blog
, to help work out which postcodes shared my cabinet, and from the BT DSL checker figures, I worked out where the cabinet was located (I've also worked out that the cabinet nearer to me has already got FTTC enabled, so I'm getting very impatient waiting for ours...)
Unfortunately, BT objected to the map, so that information is no longer available.