spitalfields mate get down there
The bigger wholesale markets will all stock dates - new spitalfields, new covent garden etc. Most greengrocers make regular trips so if you can't get to a market you could ask a grocer to pick some up for you. Still not that cheap though - last time I got my local greengrocer to buy some for me he was charged £5 a kilo.
Most asian & middle eastern supermarkets and delis stock them too, usually cheaper but the quality is often poor, or they're covered in glucose syrup. Try edgware road.
Ooops, sorry. Should have mentioned that. Was a bit overwhelmed when I went there too. You can get in easy enough on foot or by car but yeah some of the stall owners are reluctant to sell in smaller quantities. Sometimes you have to be quite persistent. Having exact change helps. You might need a trolley or something to carry boxes, can't remember if they provided them.
Buy them online?
Ecogreenstore UK is a middle-person, a company called SUMA sells 5kg loose pack dates for 9 quid