The majority of completions do actually tend to happen on a Friday and the last Friday of the month is generally the busiest of them all. Yet, there is absolutely nothing to say completions must or should happen on a Friday.
Essentially the completion date is one that is mutually agreed by both parties so it can be whichever working day of the week (it will need to be a working day so that their solicitors can advise when funds have been transferred / received).
A lot of people prefer a Friday completion for practical reasons, the most obvious being that many people prefer to move house over the weekend, rather than taking time off during the working week.
Likewise it also suits many people to have completions scheduled for the last Friday of the month so that their first mortgage repayment can coincide with their monthly salary cheque going in.
There's an argument that in this day and age people are in a much greater hurry to complete than they used to be. Years ago, the period between exchange and completion was a standard 28 days, but now less than one in ten transactions complete in this more relaxed and much less stressful timeframe. In fact, according to recent figures from one of the UK's largest conveyancing firms, some 40% now complete within three days, and around one in four exchange and complete on the same day!
This seems fairly logical but it can in fact lead to unintended consequences, in terms of the stresses and strains placed on the entire system. Indeed, many of those involved in the property industry, from agents and solicitors to removals firms, would be only too happy to see the burden of completions spread a little more evenly throughout the week. Even the BACS money transfer system can find itself under enormous strain. An example of which was dramatically demonstrated one Friday last October, when it crashed for nearly 10 hours, effectively putting thousands of home moves at risk.
If you are not reliant on your existing property being involved in your chain to facilitate your move then it is actually great to have a couple of days, even if only the evenings, to go in and clean and tidy up your new place before actually moving in on the Friday or over the weekend. This isn't always possible depending on your circumstances but if you would really prefer to complete on a Tuesday, say, rather than a Friday, I think you would be surprised to discover how amenable your agent and solicitor might be. The only problem, of course, being that everyone else in the chain will probably still be focusing on Friday... But, it's worth a try!