One tip is to check the vacination record the GP Practice holds, before yu get to the end of term.
DD schools (primary and secondary) were in different boroughs and health authorities to the one she lives in, and none of her school vacinations had made it onto her health records. Luckily the schools themselves were able to provide details and the practice then updated her record.
Skilltan, DD did two seperate sets of WE, arranged at reasonably short notice. Oddly the one which potentially had contact with quite a vulnerable patient group had a reasonable short list of vacination requirements, whilst the other wanted "everything", Hep B, BCG, the lot.
There was a shortage of one, some could not be adminstered at the same time as others, and BCG was a bit of a (short-course) marathon that could only just be done in time, even without the constraints of making appointments at our stretched inner-city practice.
We ended up buying our way out as a private GP centre near Harley St who claimed to be the only people in London to have the missing vacine. The doctor queried why DD was being asked for so much for a three day stint in a mainly out-patient department. Then it turned his main job was as a Public Health consultant at the same hospital. Hopefully he has since got things changed, not least because the demands were seriously expensive. (Though the work experience came up at interview and DD had lots to say, so perhaps a good investment.)
Luckily Bristol sort everything out once med students get there, which saved us a booster, but which presumably will have saved others quite a lot of money.