To update this;

The first two flower sprays didn't pollinate despite a fan blowing air
around and much finger-flicking. That's when I started reading the internet
and so started buzz pollinating with my electric toothbrush daily. Since
then I have small fruits forming on all flower sprays.

Unfortunately the tall straggly nature of cherry tomato plants means that
the plant has outgrown the available space by the third flower spray and, as
my budget is so tight I had to turn the heat off after a few weeks of no
fruit setting. So in one way it was a failure but in others it was a
success.

Lessons learned:
- Tomato plants need a certain amount of heat to fruit (=/17º C) and LEDs
are too efficient to have enough waste heat for the purposes (in my
situation).
- Cherry tomato plant retain their tall straggly growing style even in the
presence of very intense light and don't 'dwarf' like some other plants do
in the same situation. Growing single-spray ~ 3 leaf cuttings and multiple
plants would be a better option than a plant from seed for me.
- Buzz pollination is essential for growing tomatoes and in the absence of
insects an electric toothbush works very well.

I may try again next winter, growing with cuttings as outlined above and
with the LEDs in a 'light bar' arrangement so as to spread the light across
several short plants rather than using a (close to) point-source directly
above a single plant.

Another good thing to come out of this is that, now that my flowering cherry
trees are in full bloom and thick with Tuis and bees and the peach tree buds
have swollen and are starting to peek out I have several healthy cherry
tomato cuttings ready to go outside very soon (and a source for more).

I hope this experiment and the reporting thereof helps others with similar
interests.
--
Shaun.

"Humans will have advanced a long, long way when religious belief has a cozy
little classification in the DSM*."
David Melville (in r.a.s.f1)
(*Diagnostic and Statistical Manual of Mental Disorders)