If your ancestor was an enlisted man you will need to have an idea of the regiment they were in, because before about 1873 the records surviving are usually organized by regiment. This is especially pertinent if your ancestor was not pensioned, most weren’t!
You can search the National Archive Discovery catalogue by name for non-commissioned officers and soldiers listed in some of the muster rolls and pay lists from the early 18th century to 1898 as well as description books for 1756 to 1900. The description books give the age, place of birth, trade and service. You might strike lucky!
FindmyPast and FamilySearch host a collection of British Army Service Records 1760-1915, holding about a million pieces, including records of men pensioned out of the Army (1760-1913) or who served in militias (1806-1915). You should discover between four and eight pages for Army or Militia with name, place of birth, regiment/s, year of discharge and dates of service. Sometimes you’ll get a physical description and information on family members.
Back to The National Archives there will be militia regiments records from around the middle of the 18th century, but as I mentioned you will probably need to know the name of the regiment to search for an individual. As well as these sources you might consider the Edinburgh Army Attestation Registers covering 1794-1887, at Edinburgh City Archives. These include men from various parts of Scotland and some from England and Ireland, who enlisted not only in the regular army, but also in the Royal Marines, the East India Company Army and various militia and volunteer regiments.
Ancestry too, holds many records a free index is available to some, for instance Gateshead, Durham, England, War Honours Scrapbook, 1914-1920, “This collection is a scrapbook of newspaper clippings of photos and names of soldiers from the Gateshead area in World War I. Most of the clippings are portrait photographs of individual soldiers with information about their unit, rank and condition, such as wounded, killed or missing. The scrapbook also includes articles about memorial and awards given and there are also a few group photos”.
The Genealogist has a database of browsable books including regimental histories.
You might also consider Archive.org https://archive.org/index.php it is a bit more convoluted to search in here but all the same a valuable resource for history.
One lockdown plus has been access to The National Archive online, register, search discovery… https://discovery.nationalarchives.gov.uk/
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 Ancestry.com. Gateshead, Durham, England, War Honours Scrapbook, 1914-1920. https://www.ancestry.co.uk/search/categories/mil_lists/ : accessed 26 March 2021.