A lot can depend on the "other side". I could do it very quickly but to an extent could only move as fast as I got the information in (in a purchase), even doing as much of their side of the leg work as I could. Recommendations can be key here. Most lawyers know others who are properly independant but work quickly and efficiently (without cutting corners). People who use email are vital, so much can be done like that and having lawyers who work well together can make a big difference in cutting out more formal faff.
Some agents (if through them) can be very good in pushing matters along as well (their incentive, the quicker it goes through, the quicker they get their fee). They can form a vital direct bridge with the sellers rather than via two sets of lawyers if there is a holdup.
Most things can be done online now (searches etc...), lawyers who still use the old fashioned paper methods and rely on all formal letters rather than emails etc... will more than likely take far longer.