It doesn't really work the same as the way you'd work with a realtor in the US. You don't sign up with an agent who then looks for properties for you, there may be a small degree of that, but honestly estate agents for rental properties don't need to chase around finding people properties.
The lettings market is so competitive that properties go on first viewing if they're anyway decent at all, the reason you get the same rubbish properties coming up is because anything new that's great is going to go immediately, I've been the first viewer on the last three flats I've taken and missed out on countless others by being the second or third person to see it.
The way to do it is to have lots of websites on refresh, findaproperty, rightmove, friday ad, gumtree, ring around to all the agents in the morning and ask if anything came on the market today.
Know your absolute max budget and area. Have your money, references etc ready to go. Look for properties around your budget and just above, when you see something, ring immediately, if you can't see it that day you're probably going to lose out. Always remember you can make the landord or agent an offer, worth doing to get properties out of your price range for an acceptable price.
As soon as you see it, sign for it.