Why the Problem?
The British Royal Mint used to issue proof sets of coins only on very special occasions, such as Coronations, or major design changes to the coinage.
The first we know of was issued in 1826, and in those far off days, modern packaging and presentation was unknown. It was not until 1970 in the UK, that the Mint started to commercially market specially produced collector and gift packs of coins. Sets before then did not come with certificates or informational booklets. For some issues, we believe even boxes were an optional extra!
In some of the years, the boxes were printed with the word "Specimen", and in other years this was omitted. The problem arises because nowadays most of these "specimen" coin sets would be described as proof sets. Often owners of specimen sets do not know that what they own is a proof set. Buyers also get confused.
Over the years, many dealers or accessory suppliers have made boxes for popular dates, and many of these were made to look like official boxes, some with impressive sounding wording including the word "Specimen".
If we check the word specimen in a good dictionary, it simply means representative sample or example, and not necessarily a specially selected sample.
We have attempted here to give a simple but definitive guide to steer all through the clouds of confusion.
It may be useful to read our other page which explains:

Proof v. Uncirculated? We explain the difference between proof and uncirculated or non-proof coins.

Official British Proof & Specimen Sets

Notes
Qty = Number of coins in set.
Unofficial sets exist for many dates, including those above. These are not proof sets, merely privately collated sets from normal circulation coinage. This applies particularly to 1887, for which large numbers of retrospectively created sets exist.

Our Photographs We have shown two photographs, both of the reverse side of 2001 sovereigns. The top photo shows a proof coin, the lower photo is of an uncirculated one. It is not easy to photograph coins. The background of both coins looks a very dark chocolate brown, but in real life they are yellow. The contrast between matt and polished surfaces shows up very well on the proof coin and this allows fine details to be seen more easily, whereas on the uncirculated coin, the raised design is also slightly polished, and this results in it being more difficult to distinguish the details of the design from the background.