Name the paper before anything else
Almost every stalled request starts the same way: the sender is not sure which paper was wanted. A transcript, a company file, a court paper and a birth record are four different jobs with four different starting points. The form or letter that asked for it nearly always names the record, so read that line closely and work only from it.
A copy with somebody behind it
The slip speaks for a signature and a seal, which means the sheet you send must carry one. Westminster Register Office at 317 Harrow Road issues fresh certified copies of birth, marriage and death records, and a copy from there stands in for the certificate you keep at home. Your own certificate never has to leave the house.
That habit pays twice. A civil record lost in transit is replaced only by starting the request from scratch, and a signed copy is the one version the Legalisation Office can act on at all. Order the copy first and everything after it becomes routine, which is not true the other way round.
Why the route stops after one office
Sweden joined the Hague Convention in 1999 and Britain was already inside it, so both ends of this corridor recognise the same slip. Document legalisation for Sweden therefore ends with the British mark, and an apostille from United Kingdom to Sweden has nothing stacked above it. One office, one charge, one envelope out and one back.
What to have ready, and in what order
So what you need for an apostille for Sweden is short: one signed public version of each paper, the British charge of £45 per document by post, and room for the post itself. A registered business can use the next-day line at £40 per document instead. Nothing further is asked of you on this corridor.
Order matters more than speed. Getting the register copy in hand is the slow part and it is entirely within your control, while the marking is a fixed published step that runs the same way for every sender. Sort the sheet out first and the rest of the job looks after itself.