I needed travel insurance upon arriving here, so I've done this. Among your best options, depending also on age, and I have not read the recent fineprint, but someone once told me that STA might offer what you need.
See:
http://www.statravel.co.uk/cps/rde/xchg/uk_division_web_live/hs.xsl/travel-insurance.htmIn all likelihood, you'll need to call places to do single trip insurance--as opposed to paying for annual coverage like many folks do. I know Aviva will do it--but with higher costs as noted by Olive. But, I'd also call Directline. (I did it through Aviva--but in connection with my bank and with other perks... and they just changed these rules last month...argh)
You absolutely MUST call. Do not fill out an online form and think it's ok. Because there is a lot of fineprint, and in this situation you need to speak with an agent.
Best of luck and do let us know on this thread how it is resolved.