Things to watch out for when looking for property in London:
Rent is typically expressed per week rather than monthly. Monthly rent is actually 4.3 weeks rather than 4 weeks because there are 52 weeks in a year.
Some landlords are flexible with furnishings, curtains, linens, etc. Ask your agent about these things when you are looking at properties.
Look for storage space/closets as many London flats do not have such space built in.
Be aware of the washer and dryer situation when looking at properties. Most units have a combined machine, however some simply have a washing machine. Separate machines do exist, but they are rare. You may be able to purchase a dryer if given approval from the landlord and you have the space.
Check the shower pressure if you are serious about a property. The higher up the unit, the lower the pressure may be.