Make a rectangle with specific width and height

After setting an A2 size sheet with dimensions in
mm, how can I draw a rectangle with a specific
height and width?

I want to have a rectangle which is exactly 25mm
in width and 50mm in height.

Have tried using the mouse to construct the rectangle
but cannot get an accurate result for the specified
dimensions.

which version of LC do you use?
In 2.2.2-alpha branch there is a command that allows to create rectangle with given width and height (version is located there : https://github.com/LibreCAD/LibreCAD/releases/tag/2.2.2_alpha-latest)

There are several ways to achive this (yet first ensure that the units for drawing are metrict and mm).

1) enable snap to grid and check snap size - with proper snap step, you'll be able to draw a line by mouse.
the mouse widget or informational cursor will provide you with hints for the current mouse coordinates and relative distances.

2) you can use the command line.

given that your lower left corndr is in 10,10, you can type something like:

line
10,10
@25,0
@0,50
@-25,0
@0,-50

The form of coordinates as above relies on relative coordinates, yet of course it is possible to use absolute ones.

3) Alternativele, you may use CTRL + arrow shortctut with providing direction.

I.e, to draw a line with length of 50 from left to right, you may type someting like (where CTRL+RIGHT etc. is shortcut, of course)

line
10,10
25 CTRL+RIGHT
50 CTRL+UP
25 CTRL+LEFT
50 CTRL+DOWN

4) in 2.2.2 alpha, you may use Rectangle 1 Point command and specify the width and height of rectangle  in tool options.

Most of these ways above are applicable for non-rotated rectangles.

For rectangles that are rotated (so are not parallel to x and y) - the simplest way is either use Rectangle 1 Point command (that allows to specify rotation angle) or rely on specifying custom User Coordinate System (that supports offset and rotation) - yet the later way is supported by 2.2.2 alpha only

I am using LC 2.1.3.   I find the using the mouse is not accurate enough for me.
And would need to enter the exact size.

hm... not sure your point regarding mouse that is not accurate. Mouse position depens on the calculated snap point (that is determined acccording by enabled snap modes), so in most casese it's accurate enough.

Yet if needed - use entering coordinates as I've mentioned above via Cmd widget command line... Here is  up to you which particular coordinates are entered.