Chris,
A cash buy can be done in even less time. I bought a property few years ago as a cash buy, so no waiting around for the lenders, completed searches and general conveyances and exchanged on the ninth day.
For the more “normal” purchase i.e. where I'm taking loans, I can still complete within a 28 day cycle by “pushing” people along and staying on top of things. I use a postal conveyance company now and not only is it cheaper, it's fast as they know my needs. The secret here being that you are up front with everyone concerned and they are made aware of any time lines you have. Also, it gives you a good bargaining chip when you stress that they get your future business…
Having arranged the money “in principle” with a lender will also decrease your buying time, especially if you are a known customer…
Regards,
Malik