It's a joy.....
One main difference in Estate Agents between the US and the UK is that as the buyer/Renter you don't really have anyone working for you.
Definitely call multiple agents, because that is the only way you will see a good selection of properties. They will normally take your details, suggest a few properties to view that are on their books currently and then they will start sending you all sorts of crap that doesn't meet the criteria you specified. It really does work out that you have to be looking for a needle within a haystack.
If you are renting: They won't want to talk to you more than 4 weeks from your move date. The only fee you should have to pay is a credit check. I think the one we paid 2 years ago was £50 for each person. Once you find a place and the credit checks go through, you will need a deposit to secure it. Depending on the agent this could be £100 non-refundable or the whole 4-6 weeks deposit required by the landlord, refundable if everything doesn't go through.
If you are buying: You will generally work with one contact person at each office, but not necessarily. They don't generally go out of their way to show you properties, i.e. past 6:30 in the evening or on Sundays. They often times just give you the address and you have to go to the flat/house and be shown around by the owner/tenants. Awkward! I don't think as the buyer you have to pay anything to the agents, because your solicitor does most of the work re: mortgage, surveys etc.
I would say in both situations you will find that you do most of the leg work finding suitable places to view. Sites like propertyfinder and a findaproperty will be your new favorite websites!
Good luck!