Hi Sarah,
Welcome to the Moms Panel, it's so great to see questions from my side of the pond :-)
There are several character restaurants that are outside of the parks, the most popular, and the one I'd recommend for your family, is Chef Mickey's at the Contemporary Resort. This is a buffet restaurant and plays host to Mickey and his friends, they can vary but you will often see Minnie, Donald and Goofy there. As it's a buffet you'll find food to suit all the family and meeting Mickey is a fantastic way to start your holiday!
Another option is 1900 Park Fare at the Grand Floridian Resort, this is also a buffet and features Prince Charming, Cinderella, her Step-Mother and 2 Step-Sisters. My children love this restaurant and find the characters hilarious as they really interact with them! You can get to both resorts by catching a bus to the Magic Kingdom and then boarding the resort monorail.
You can see details of both restaurants by clicking
HERE (if you get redirected to the UK website simply click the "visit US Site" link in the top left hand corner and retry) and then choosing "character dining" from the drop down list "dining experience". You can book up to 180 days in advance, which I highly recommend you do, either online or by calling 001-407-939-3463.
If you are arriving at WDW directly from the UK I would actually recommend you don't start your trip with a big meal as you will be extremely tired. Whenever we arrive we force ourselves to have a swim and a light meal and normally fall fast asleep by about 8.30pm EST which is 1.30am GMT. We really wouldn't enjoy a character meal and prefer to save it for another day when we're wide awake!
I hope that helps and you have a fantastic trip,
Jo