What is the likelihood that the connection speed is going to rise without me calling BT again?
That isn't the main problem (the solution is likely that described by Mr Saffron, but not certain).
Your real question should be: "When the connection speed returns to a normal (high) speed, what is the likelihood it will drop again?"
Answer: Extremely high.
This is because you appear to have an extremely unstable line, which is dropping out for unknown reason - but likely to be noise on the line. Whatever the cause is, it looks to be intermittent, so is the hardest kind of fault to find.
Ordinarily, I'd suggest you used a program to monitor your modem statistics. It's a while since I did much with ADSL modems, so I'm not sure which works best with the Home Hub 3 ... but this one seems compatible:
http://www.vwlowen.co.uk/RouterStatsHub/routerstatsh...
Can you *hear* any noise on the line?