No, it's not a limiting factor - and even if it were, the Juries Act 1974 grants courts a special power to require people in the local area (passersby/office workers/etc.) to serve as a jury member without written notice if a jury is incomplete. This is sometimes known as 'praying a tales(man)'.
If it appears to the court that a jury to try any issue before the
court will be, or probably will be, incomplete, the court may, if the
court thinks fit, require any persons who are in, or in the vicinity
of, the court, to be summoned (without any written notice) for jury
service up to the number needed (after allowing for any who may not be
qualified under section 1 of this Act, and for excusals and
challenges) to make up a full jury.
§6 Summoning in exceptional circumstances - Juries Act 1974
Reduced jury sizes would, however, allow trials to proceed in courtrooms where social-distancing procedures in response to the COVID-19 pandemic cannot be adhered to with a full twelve-person jury. The House of Commons Constitution Committee has published a report on the impact of COVID-19 on courts and tribunals in England and Wales - Lord Burnett gave evidence to this committee on this topic and offered two other possibilities: Judge-only trials, and trials with two magistrates and a judge. On reducing the jury size in particular, however, his concern is the social-distancing guidelines due to the COVID-19 pandemic, rather than the availability of jurors.
Trials by judge alone would undoubtedly be quicker than trials by
judge and jury and present few problems with social distancing. Their
main disadvantage is that they would dispense with the involvement of
lay people, which is the hallmark of jury trials. Trials by judge and
two magistrates of either way cases would retain that lay involvement
to some extent and be quicker than those involving a jury. They would
also present few problems with social distancing. The Chairman of the
Magistrates’ Association has expressed support for this option.
Either of these options would undoubtedly provide a practical way of
clearing cases more quickly. The reduced jury numbers option has an
historical precedent in the Second World War when, save in capital
cases, the number was seven. It would enable some courts to be used
for jury trials which are too small to use with 12 jurors even with
practical adjustments and might therefore contribute to accelerating
the trial of some cases. All these options need careful thought and
informed debate.
The Rt Hon The Lord Burnett of Maldon – written evidence (CIC0045)
Another point brought up by Justice Secretary Robert Buckland, giving evidence to the same committee, was that social distancing must be adhered to not just in the courtroom, but during the selection process, which of course requires more than twelve jurors:
Covid presented particular challenges, and I would have made far too
cosy a set of assumptions if I had ignored the realities of social
distancing and the likely effect not just on the health of jurors but
on their sense of safety coming into the court as a result of a
summons.
...
Those who have bothered to observe my thoughts and public expressions
over the last few months will have noted that from the outset I aired
the possibility of what I call wartime juries—that is, reduced numbers
of jurors rather than a departure from the principle, for example to a
judge and two magistrates. The retention of the jury principle is more
important to me than anything else. That is why I am prepared to look
at jury size where we have nine jurors, with a minimum of seven,
replicating the rules about majority verdicts on juries of 12. I can
see that measure reducing the need for larger jury panels in court and
the need for as many people to assemble to be selected by ballot.
Uncorrected oral evidence: Constitutional implications of Covid-19 - 22 July 2020
However, in the evidence given to the committee on this matter, I can't find any reference to the availability of jurors - except in the context of their reticence to serve due to fear of inadequate social distancing - being a limiting factor.
