Upvote:2
Does the British High Commission provide any emergency travel document,
No, British consulates would only issue travel documents to British citizens or British subjects. Some exceptions could also be made for refugees who received permission to relocate to the UK. None of those apply to your situation.
I see the following solutions to your conundrum:
- Ask the British consulate to return your passports prematurely without a visa, forfeiting your application.
- Ask the Afghan consulate in India to issue you an emergency travel document and use it to travel back to Afghanistan
- Wait for the visa to be issued and sort out the exams issue later on, perhaps using your passport stamps and the UK visa to prove you couldn't return prematurely