Background
As I understand it, the function of tags is to allow questions about particular topics or events to be found quickly. As such, we should probably be careful of removing tags which help to find information. The numbers of questions may be relatively small now, but they will hopefully grow as the site grows.
In this case, the problem is not a straightforward one, and is complicated by history, geography and politics. The language matters to a lot of people (note the history of nationalism in Ireland, Scotland and Wales!) The following diagram will give some illustration of what I mean:

And even that does not capture the full complexity! I hope that I don't tread on too may toes in what follows. If I do, I can only apologise and hope that I have only trodden lightly!
I think there are logically two ways to look at this if we are going to decide what tags are likely to be needed to capture this complexity: top-down or bottom-up.
I'm going to try a bottom-up approach.
In its modern sense, "Britain" is a rather nebulous, often ill-defined term. However, when that term is used the component parts that go to make up the whole will probably be some, or all, of the following:
When James VI and I succeeded to the throne of England on the death of Elizabeth I in 1603, he had three separate and distinct crowns: the crown of England, the crown of Scotland and the crown of Ireland. The term Great Britain was actually first used during the reign of James VI & I as a kind of shorthand to refer to the (then still separate) Kingdoms of England and Scotland.
The Kingdom of Great Britain was created by the union of the crowns of Scotland and England. The name was defined in the first sections of the Union with Scotland Act 1706 and the Union with England Act 1707.
So, for example, the 1706 Act states:
"That the two Kingdoms of England and Scotland shall upon the First day of May which shall be in the year One thousand seven hundred and seven and for ever after be united into one Kingdom by the name of Great Britain"
Which left two kingdoms: the Kingdom of Great Britain and the Kingdom of Ireland.
On a side-note, Wales had been conquered and occupied by Edward I in the 13th century, and was effectively a colony of England until it was formally annexed through the Laws in Wales Acts 1535 & 1542, which made it a part of the Kingdom of England. This is also why there is no "Welsh" component in the union flag:

and may also explain why we have relatively few questions explicitly about Wales so far, and don't (yet) have a tag for it.
In 1800, the Union with Ireland Act united the kingdoms of Great Britain and Ireland. The act states that:
"the said kingdoms of Great Britain and Ireland shall, upon the first day of January which shall be in the year of our Lord one thousand eight hundred and one, and for ever after, be united into one kingdom, by the name of the United Kingdom of Great Britain and Ireland"
The name was amended to the United Kingdom of Great Britain and Northern Ireland when southern Ireland became independent of the UK from 1922.
So, what I suggest is the following:
On the basis of the history set out above, I think it makes sense to retain the great-britain to refer explicitly to events involving the Kingdom of Great Britain, and to create a usage excerpt and summary to reflect that. The britain tag really does not mean the same thing.
The tag united-kingdom should be used to refer to the Kingdom of Great Britain and Ireland (from 1800 - 1922) and/or the Kingdom of Great Britain and Northern Ireland (from 1922 - ). The usage excerpt and summary for the tag should be updated to reflect that.
Which still leaves us with a couple of problems. The first of these may be illustrated by a couple of examples. How should we tag questions that are explicitly about Roman Britain (distinct from the rest of the Roman Empire), or about post-Roman Britain before the emergence of an entity that was recognisably "England"?
It is in situations like this where the less-precise term britain may be useful. However, it is probably better to use the unambiguous british-isles, with an appropriate usage excerpt and summary to make it clear that the function of the tag is a "catch-all". We can then maintain britain as a synonym for british-isles.
A quick glance at the list of questions tagged britain shows a number that should probably be re-tagged as either great-britain, (e.g. Why were British ships not of the same quality as French and Spanish ships until the latter part of the 18th century?) or united-kingdom (e.g. How did the Crimean war change British society?)
The other problem is Ireland. We currently have ireland and republic-of-ireland. The former states that:
The questions may refer to both the island itself and Ireland as a country.
While the latter currently has only 4 tagged questions.
It may be that we should consider having three tags:
- ireland: for questions referring to the island of Ireland or
the Kingdom of Ireland until 1800
- republic-of-ireland: for questions about the Independent
republic of Ireland from 1922
- northern-ireland: (probably with the tag synonym "Ulster") for
questions about Northern Ireland after 1922.