This is probably something which different airlines may have different rules (a bit like flying when pregnant). Had a quick look on Virgin & BA websites, nothing specific is mentioned age wise.
Some other things you may also need to take into account are:
Getting the birth certificate
Getting baby's passport
Getting health insurance for baby
6-week check
Immunisation dates
and of course booking the flight, which I do not know if you can do prior to baby being born considering whether the sex is 100% confirmed (scans have been known to be wrong) and if you are firmly decided on names.
HTH