One of the fine cliches of comparing life in Great Britain and the USA is that they are 'two nations divided by a common tongue'. I'm not going to get into a "how should Leicester be pronounced" thread here, but one of the differences between the two is that over there the common acronym for our communities is GLBT, whilst over here it's LGBT.
The American model kind of makes sense as a historic series of expansions. As the range of identities seen as core to our movement fragmented and acquired respect, Gay became Gay and Lesbian became GLB became GLBT.
The British one however has a peculiar hiccup. Gay became Lesbian and Gay, with the women put in front since within L&G spaces they tended to be marginalised and the minority, despite the hypothesis that there should be more lesbians than gay men in a country where the census records more women than men.
So you're putting the more marginalised group in the front of the acronym to avoid them getting dropped off, and people lapsing into talking about "gay" when meaning "lesbian and gay".
Then, just as across the pond, we add in the B and the T.
Only we add them at the end. The "you need to worry less about making sure you include these bits, people will just imply them" end. B got in there first so it's LGBT.
Which doesn't really make sense for two strands of the LGBT rainbow that have less visibility, credibility, accessible community, money, and so forth, than the lesbian strand. B and T folks clearly belong at the front.
Whether following the British logic it should be BTLG or TBLG could no doubt be a long and heated debate: I can see arguments in both directions though for me the fewer support groups and social spaces for B give it the edge.
By now we've been talking about LGBT for so long that the battle of which order the letters should flow in is long since over, but whenever people um and ah about going for the UK or USA ordering, I'd suggest you put the four letters in a Scrabble bag and pull them out one by one to decide.