Right, there are couple of different issues rolled up here (who can be in a group, and what a group is), so let's break it down.
Firstly, if you have an exclusive¹ group that is covered by the Equality Act then whatever the inclusion characteristics are must all be shared by everyone in the group.
So an LGB group for people who are same sex attracted would include lesbians, gay men and bi people of both sexes. It would also include trans people who are attracted to people of their own biological sex. It would exclude trans people attracted to people of the opposite biological sex.
A T group for people covered by the gender reassignment characteristic would include trans people attracted to either sex, but exclude LGB people who are not trans.
An LGBT group includes people with a mix of characteristics, and not everyone will share all of them. So it's not allowed.
So your initial concern is not unfounded. You cannot have an exclusive¹ group that is covered by the Equality Act that includes all of LGB and T.
But.
You could have an LGB group and a T group who hold joint events. (If anyone challenges the legal technicalities you might also need to hold some separate events, to show clearly they are separate groups - but it's unlikely anyone would get that nitpicky. Just having separate membership lists is probably enough.)
Or you could have an LGBT group that is not covered by the Equality Act.
Groups only count as 'associations for the purposes of the Act' if they have 25 or more people and have membership criteria.
An LGBT and allies group (or event, service etc) that was aimed at LGBT people but let anyone join in, would be absolutely fine.
A group for 'people interested in the LGBT lifestyle'² would be fine.
So technically it does cause some difficulties for mixed groups, but there are workarounds if people want them.
¹ In the sense of including people with certain protected characteristics and therefore excluding people without them.
² Whatever that might mean - it can be as broad as Stonewall's umbrella.