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War memorials were mainly constructed after WWI to commemorate the troops who gave their lives in the war. Many were then updated after WWII. Some war memorials date back to the Boer War. Almost every town and village in Britain has a War Memorial. They take many forms, the commonest being an obelisk, a cross or statue of a soldier. Some commemorate the inhabitants of a place, some are for schools and others are for companies or Military groupings.
Many memorials are grade II listed, 61 are II* listed, Link*_listed_war_memorials_in_England
& 12 are Grade I listed. Link
A search for memorials can be carried out at Link

Listed buildings and structures are officially designated as being of special architectural, historical or cultural significance. There are over half a million listed structures in the United Kingdom, covered by around 375,000 listings.
Listed status is more commonly associated with buildings or groups of buildings, however it can cover many other structures, including bridges, headstones, steps, ponds, monuments, walls, phone boxes, wrecks, parks, and heritage sites, and in more recent times a road crossing (Abbey Road) and graffiti art (Banksy 'Spy-booth') have been included.

In England and Wales there are three main listing designations;
Grade I (2.5%) - exceptional interest, sometimes considered to be internationally important.
Grade II* (5.5%) - particularly important buildings of more than special interest.
Grade II (92%) - nationally important and of special interest.

There are also locally listed structures (at the discretion of local authorities) using A, B and C designations.

In Scotland three classifications are also used but the criteria are different. There are around 47,500 Listed buildings.
Category A (8%)- generally equivalent to Grade I and II* in England and Wales
Category B (51%)- this appears generally to cover the ground of Grade II, recognising national importance.
Category C (41%)- buildings of local importance, probably with some overlap with English Grade II.

In Northern Ireland the criteria are similar to Scotland, but the classifications are:
Grade A (2.3%)
Grade B+ (4.7%)
Grade B (93%)

Read more at Wikipedia Link