DH and I got our flat through rightmove, and we had great success. We saw a property on rightmove we really liked, contacted the agent right away, and set up an immediate appointment to see the property. We gave a deposit the same day to hold the place, and it's been almost a year and we're still here.
Be aware though, properties listed on rightmove may not actually be available due to the frequency agents update their listings and how quickly properties go if they're good. I've called agents about flats that were available on rightmove to find out they had already been taken, sometimes even hours after the listing was submitted. So, don't get your heart set on a place you see online as it may not even be available. But it is a great way to see what agents operate in what areas - you can then find their sites and see if they have anything similar to what you're looking for, and/or start up a conversation so they can update you as soon as properties become available.