I'm making Christmas brunch but neither my Mum or brother eat eggs (they only eat them when incorporated into cakes etc.). Would love some ideas!

A breakfast casserole like one I posted on the site: https://food52.com/recipes/19821-sinful-chocolate-hazelnut-cinnamon-french-toast-bake

So many similar recipes online with different flavor profiles.

It might be fun to do some Scandinavian style open face sandwiches. You could have good ham and good butter, perhaps garnish with a very thin slice of cucumber; smoked salmon and either ricotta or quark, garnished with fresh dill; roasted vegetables and cheese garnished with a little bit of preserved lemon.
For a make ahead, how about tamale pie? Chorizo, corn, tomatoes, chiles, olives, etc. can all be added to your taste. It can be baked ahead and reheated, or just held in the refrigerator and baked before you are ready to serv.

I'd say popovers, with soft butter and jams, and a large fruit salad and sausages for the sides. Popovers look impressive and are oh so delicious. As a bonus, popovers go in the oven and sausages on the stove, so no issues about keeping everything warm and ready and competing for space.

http://www.foodnetwork.com/recipes/melissa-darabian/fool-proof-popovers-recipe.html

There are tons of kugel dishes (baked noodles with different things in them), sweet or savory.
Same with bread puddings, sweet or savory.
Any of these could take pride of place at a celebratory brunch...then top with things, or have a buffet choice of things your family likes to top them off...fresh fruits, fruit syrups, applesauce, nuts, whipped cream, mascarpone, hard cheeses, chopped fresh herbs, chutneys, jams, onion marmalade, and so on.
The toppings will not only add flavor but color to these dishes----which often have the yellow brown color of waffles, so need a color boost.
The garnishes

Also left out biscuits & gravy, breakfast burritos/enchiladas/tostadas, avocado toast, crepes, an array of pastries, hash, and almost any sandwich or wrap can be eaten for breakfast.

Will they do a frittata?

Look at the most recent contest-- big breakfasts-- lots of ideas here. https://food52.com/contests/434-your-best-festive-crowd-feeding-breakfast

DO you want sweet , savory or both? Croque Monsieur is a nice brunch treat, Maybe a cheese board with fig spread .

lox and bagels with all the fixings! (capers, tomatoes, cucumbers, cream cheese)

how about French toast and/or waffles made with unsweetened batter, made ahead and kept warm in the oven, set out with an assortment of both sweet and savoury toppings for people to add as they like. A couple of syrups, cheese, fruit, lox and cream cheese, proscuitto, sauteed mushroooms - you get the idea.