I don't think being fair necessarily means spending the same amount of money on everyone all of the time.
And no, I don't spend the same amount of money on my relatives and I don't have an even flow back either.
Someone did suggest the bike might be used for commuting - is this a possibility? A present to enable someone to get a better job or just to stay in their current job is very different to a casually expensive shiny toy.
If there's a back story of your dad always spending money on your brother and not the rest of you because he harbours some kind of 'boys are best' attitude, then I completely agree it's shit. However, I can't deduce that from one gift in isolation.
The other thing to consider is, if you needed an £800 bike and had no means to buy one, do you think your dad would buy you one? I mean, if you don't need a bike now, it's churlish to get upset, but if you think your dad wouldn't come through for you in the same way if you needed... that I get.
It's a bit like money for university or a wedding. Siblings might be in equal need of contributions... but not at the same time in their lives. He's not buying you an expensive toy now... but will he buy you one a few years later?
You mentioned you don't need someone to buy you stuff, because you earn your own way. TBH, I'd just feel proud of that. Your brother clearly doesn't have the same attitude, and I think yours is better. You can stand on your own two feet. I think that's worth more than a bike.