What is being compared, and to what
An apostille is a certificate attached to a document, confirming that the signature or seal on it is genuine. The Legalisation Office holds specimens of the marks used by the bodies it recognises, and the whole of its work is holding your sheet against one of them. That is the mechanism, and it explains almost every rule that follows from it.
So what you need for an apostille for Latvia is a page bearing a mark from a body on that list. A sealed copy from a register qualifies. So does a court seal, or a signature from a company officer whose specimen the office can find. Nothing about your circumstances enters into it.
Why so little of it involves you
People arrive expecting a process built around proving who they are, and find one built around proving who signed. An apostille issued in Coventry for use in Latvia does not describe you, your plans or your reason for needing the sheet, and the certificate carries no view on any of them. It is a narrow, technical statement about one mark on one page.
This is also why the route is done at arm's length. The Legalisation Office covers the whole country by post, so no appointment exists to miss and no counter exists to travel to. The paper does the moving; you do the posting and the waiting.
What Latvia does with the result
Latvia joined the Hague Convention in 1996, so an apostille for Latvia is the correct and sufficient certificate and no consulate takes any part in the route. Document legalisation for Latvia therefore ends at a single desk. A reader there sees a certificate they recognise on sight, checks that it sits on the page it names, and takes the signature underneath as genuine.
That is all the certificate is asked to do at the far end. Whether the contents suit the purpose is a separate judgement made by whoever holds the file, and an apostille from United Kingdom to Latvia neither helps nor hinders it. Getting the right document is your job; proving the signature on it is the office's.
What that means when you set the file up
Spend your effort on the sheet rather than on yourself. Make sure it comes from a body whose mark can be matched, that it is unaltered, and that the names, dates and places on it read correctly before a fee is paid. A page that fails on any of those counts fails no matter how well the rest is organised.
Coventry Register Office prints certified copies of the civil entries registered in the city, so the certificate you keep at home need never travel. Order as many copies as there are bodies that will end up holding one, since each finished sheet is bound to its own certificate and cannot be divided later.