"it has to be a hospital birth as my first labour was quite fast and this baby looks to be quite big*"
*
Neither of these things require a hospital birth; have your caregivers explained their reasoning?
If they think you're likely to have a second precipitate (fast) labour, it may be a better idea to plan for a home birth, rather than risk a) stalling a naturally rapid labour by transferring in at a late stage or b) delivering in the ambulance/car park/lift on your way to the hospital.
FWIW, I've had six at home, 5 in water (mostly in the bath, once in a pool - much more comfortable!), and have very quick first and second stages (contractions/pushing).
One of them, they thought she'd flipped to breech during labour, and were strongly encouraging me to transfer in; I'm glad I didn't, as less than half an hour later she was born - head first! It's highly unlikely I'd have made it onto a hospital bed before delivering.
N.B: labours that happen quickly are generally very straightforward; if there are problems, these tend to slow labour down rather than speed it up.
N.B2: I'd take no notice of size predictions, based on scans or any other kind of measurements, particularly later on in pregnancy. These are notoriously inaccurate - certainly not a reliable basis on which to make clinical decisions about your care at this stage of your pregnancy.