Dermot Carroll wrote:

"...However I assume that the shower tray would then start filling with
water
every time the bath was emptied due to the higher level of water in the
bath..."

I have a similar situation relating to a bath and bidet. OK, the bidet
outlet is a bit higher than that of a shower tray, but the bath water
level is regularly way above that of the bidet outlet and I've never
had a problem with bath water backfilling the bidet.

I should imagine that the key factors are the relative flow capacities
of the bath outlet and the length of pipe that leaves your bathroom.
Let's take an extreme example... If you had a bath and shower tray
close together connected to a very long run of shared outlet pipe (such
that the length affected the flow rate), then you might expect the bath
to fill the shower tray unless you took steps to restrict the flow from
the bath (such that it couldn't deliver more water than the long pipe
run could cope with). In an even more extreme example imagine if the
flow in the common part of the pipe is blocked. In that situation the
bath water WILL flow back into the shower tray until it reaches a
common level - something you obviously want to avoid. At the other
extreme, imagine a bath and shower tray connected to a very short
common pipe run... As that pipe run gets shorter and shorter, it has
less and less effect on the flow. Eventually the flow rate is limited
by the bath outlet and trap, at which point it becomes impossible for
water to backfill the shower tray.

In my limited experience, provided that you use swept joints the right
way round and the bath and shower don't share a long common length of
pipe, and you don't encounter any blockages in the common part of the
pipe run, there isn't a problem. If anything, I've found that the
emptying of the bath creates suction at the bidet and sink such that
there's a tendency for the water in their traps to be sucked out by the
flow from the bath. Of course, although I haven't found this a problem
in practice, this may be something you would want to avoid - and
there's probably a regulation somewhere that relates to the
effectiveness of traps and maybe even prohibits this sort of
installation.

If you really don't want two separate drains I'd be inclined to test
it. Tee into the existing pipe with a trap and outlet at the position
where the shower tray is to be sited, fill up tha bath and see what
happens.

Just my experience... and if you haven't already guessed, I'm not a
plumber so you may want to disregard what I've said!

Mike