We have indeed mostly been on 09 at Heathrow in recent weeks.
The changes to London City departures this week were due to the unexploded bomb found by Bromley-by-Bow tube station (covered in the press) which all week led to a 6,000 feet Air Exclusion Zone, LCY westerly departures were vectored (ie given special non-standard instructions by radio) to go all the way west to overhead the City before heading onwards. This impacted on inbound Heathrow traffic as well, once they were back on westerly arrivals, which was also being given different routes.
Next week, back to normal.
I've noticed one or two odd paths over my house lately - is it normal for aircraft to be so low and so close to LCY, but going almost perpendicular?
Very common. Aircraft going across East London north to south will pass overhead the London City VOR radio navigation mast. You will often see them change course immediately after passing overhead as they then head for their next navigation point. They cannot be above 3,000 feet in East London as that is reserved for Heathrow.
This weekend is the best of the year for such traffic as it is the Biggin Hill airshow. There has already been various traffic going over. Look out for all the old classics heading northwards this evening (Sunday) going home to Duxford and elsewhere. If they're old RAF classics from WW2, give them a little cheer as they go over - or a big wave. Yes, they can see you from low level. And they're looking out for it.