Does the Law Society (UK) state a recommended time to leave between
exchange and completion?
Yes, but only indirectly and as a "general indication" which can be easily departed from.
The Law Society Conveyancing Protocol is compulsory for members of the Conveyancing Quality Scheme and optional (but widely followed) for everyone else. Even where it is compulsory, it can (and must) be departed from where doing so is in the best interests of the client, or to comply with specific client instructions. Note that the link you posted in your question is merely an introduction to the Protocol and not the Protocol itself.
The Protocol at Step 13 of Stage B on page 17 provides (emphasis added):
Prepare and submit to the buyer’s conveyancer a contract bundle, which
includes: (1) The draft contract: (a) incorporating the latest edition
of the Standard Conditions of Sale; and (b) only with such additional
clauses as are absolutely necessary for the purposes of the
transaction;
Clause 6.1.1 of the Standard Conditions of Sale (SCS) provides:
Completion date is twenty working days after the date of the contract
but time is not of the essence of the contract unless a notice to
complete has been served.
The Protocol states at paragraph 1 under the "Interpretation" heading on page 3:
- Timetable for exchange and completion
Every transaction is different, and the time it may take for each
stage in the transaction will be different. Moreover, the timetable
that will be expected by the parties at the outset may change and the
order in which processes are undertaken may alter. There is no
‘normal’ transaction and you should communicate this to your clients
who need to be made aware that timetables are often set by third
parties and the original timetable is no more than a general
indication.
Note that the SCS itself foresees at clause 4.3.4 the possibility of amending the default timescale in clause 6.1.1:
If the period between the date of the contract and completion date is
less than 15 working days, the time limits in conditions 4.2.2, 4.3.1
and 4.3.2 are to be reduced by the same proportion as that period
bears to the period of 15 working days. [...]
Specific clauses of the Standard Conditions of Sale (SCS) can be excluded or amended by way of special conditions in the contract (e.g. "Clause X is excluded from this contract"). As you have noted, it is common and acceptable for the parties to agree a different completion timescale.
