As far as I'm aware, it should be fairly easy to get an appointment... all you can do though is create an account, try booking one and see what dates come up as available. New appointments are only released 6 weeks in advance so right now, you can book up to about September 8th.
You have almost 5 more months left in order to book and attend an appointment (or to get the application in the mail), so there's no need to hurry unless you are desperate to get your ILR right now.
Last year, there was a problem with third parties purchasing all the appointments and then selling them on at higher prices, so all the appointments would get booked up weeks in advance and you would literally have to book one as soon as it became available - at midnight, 42 days ahead. However, UKBA stopped these third parties and now there shouldn't be any problems getting an appointment when you need one.