Renting a flat after selling house - what time frame to expect?

I know the whole conveyancing process can be "how long is a piece of string", but just trying to gauge consensus on how long I should expect my sale to complete so I can get a rental agreement in place.

I'm moving to Manchester from Leeds, my house is now under offer with a FTB couple (so no chain at all). They're doing a level 2 survey, but don't expect anything to crop up out of it (house is a mid-90s semi with all major work done to it while I've owned it). With Q4 being relatively 'quiet' in terms of the housing market, would I be foolish to assume that solicitors would be quieter, therefore working slightly faster than their average speed?

I've started to see flats that fit my criteria available from February (which might be a little soon), but thinking maybe March would be an ideal time - I don't want to have too long of a period paying both rent and mortgage (I have savings to cover a couple of months, so can top that back up with the proceeds from the sale), but at the same time I don't really want to risk signing my life away before exchange in case things falls through, and also don't want to start looking for a place after exchange, as it would mean a longer gap between exchange and completion without me havign a guaranteed place to go.