"Evidence" is hard to gather when the BBC refuse to disclose it (I wonder why?)
However, if you believe for a second that the full cost to the BBC of such a production, including wages and "talent" fees can be anywhere near £310,000.................
The BBC said it didn't have to answer, but it was going to anyway.
Assuming that £310k doesn't include the program budget (the question didn't ask about the program budget, and I'm sure that you wouldn't believe their answer even if they did give it), there's about a dozen people working on the program (they were named at the end), so say a rate of £500 per day over 8 days, plus hotels/food/plan expenses of about £1200 each and you're looking at under £70k. Add £20k tops for equipment. That's for the final and the two semifinals, and assuming 8 days on site - and some of them working will be in London.
The cost of "talent" - namely Norton and Bruce, but also that pair from the semis, will be hard to separate from their other shows, and certainly isn't an incremental cost. Ken Bruce will certainly be on under £200k, so even 1 week of his time would be £4k (and he was doing his show anyway). Graham Norton's contract is
apparently on £4m for 3 years, or £25k a week.
Add that £120k budget to £310k membership cost and you're looking at 3 hours of BBC1 on a Saturday night for under £500k, or nearer £150k an hour - with 7-9 million viewers. Compare this with Doctor Who or Sherlock, which will cost well over £1m for a 45 minute program (typical 45 minute US shows cost $2-5m per episode).
These figures are most likely over-estimated in the eurovision case, and under-estimated with the dramas.
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As for the Austrailia question, this map from gcmap.com shows a line from France to Cyprus passing 90 miles off Austrailia.