Rob wrote...
I want to concatenate text in three columns, which would normally be simple.
However, if we take the cells across the three columns, each contains a set
of data using carriage returns (Alt-Enter).

To put some context on the problem, A is First Name, B is Middle Name, C is
Surname.

The data would look like:
A B C
1 David Robert Hughes
Mark Dave Marriott
Martin Benjamin Murray
2 Shaun Andrew Flannagan
Alison Jane Martin

So I would like to combine the data into some sort of output that will lead
to the following, with each :
1 David Robert Hughes
Mark Dave Marriott
Martin Benjamin Murray
2 Shaun Andrew Flannagan
Alison Jane Martin

It is worth noting that some cells may contain 5 entries using carriage
returns, while others may have 2.

This isn't possible without using temporary cells to hold parsed
individual names from each cell. Which leads to the inescapable
conclusion that what you have is a horrible data structure. Is there
any good reason different individuals' names aren't in different rows?

If you need to keep this data structure, then all you really need are
formulas to parse each cell into separate names in different cells. For
example,

F7:
=LEFT(A1,FIND(CHAR(10),A1&CHAR(10))-1)

F8:
=IF(SUMPRODUCT(LEN(F$7:F7)+1)<LEN(A$1),
MID(A$1,SUMPRODUCT(LEN(F$7:F7)+1)+1,FIND(CHAR(10), A$1&CHAR(10),
SUMPRODUCT(LEN(F$7:F7)+1)+1)-SUMPRODUCT(LEN(F$7:F7)+1)-1),"")

Fill F8 down into F9:F11. Then fill F7:F11 right into G7:H11. Then
concatenate as =F7&G7&H7, etc.

If this isn't acceptable, you'd need to use VBA.