Ooh, clanger, having read this I recognise that this happened to me - 21 years ago though so lost in the mists a bit.
Anyway, FWIW - and it may not be worth much now, but this was at a very high-tech teaching hospital in New York so as good as it got at the time - my DD1 was diagnosed as small for dates, can't remember how many weeks too small she was. I am 6' tall and gained quite a lot of weight over the pregnancy and this may have been a factor in their judgment?
Anyway I had to go in for "stress" testing (I think they call it challenge testing here - where they hook you up to a monitor and put you on an oxytocin drip and look at the heartrate behaviour during contractions) weekly from about 32 weeks, more frequently from 36 weeks, and they also sometimes did "non-stress" testing where they just monitored heartrate during kicks. The nurse who used to do the testing was a really lovely person and made the whole process much less of an anxiety than it might have been otherwise.
I had actually got to just over 40 weeks when nice nurse decided the baby was beginning to show distress - an examination showed a tightly closed cervix so they did a section and she was with us about 2 hours after the test.
She was a tiny baby, only 5-11, very small for anybody at 40+ weeks, let alone someone my size, BUT DH's weight at birth was only 6lb and I have heard that that can be a significant indicator. Anyway her APGAR score was 9. She remained a tiny child, smallest in her year, right through primary school and well into secondary school but is now around 5'7 and very fit and healthy.
Lots of luck to you, clanger, hope it all turns out well for you and the baby, just remember they always have to err on the side of caution (as they did with me).