Contact whoever it is who has been handling your application so far. Ask if it is possible to move the start date, either to October or by deferring the entire year to next April. It might be easier for them, depending on how the scheme is set up, if you defer an entire year rather than arrive six months out of sync with others on the same program.
At this stage you don't need to specify why. They'll say one of three things: yes, no, or only under special mitigating circumstances. You only need to explain your health problems if it's the final one.
If it's a straight no you'll have to consider what impact your health issues will have on your ability to function without your usual support network around you. You may also need to check things like the availability and cost of any medication you'll need.