Hiya, interesting topic and something I firmly believe in, so first, well done for picking this up (and savvy use of MN 
)
Having just had my first DD my views are as follows:
Hospital discharge - it could help if the hospital discharge included a reference to the the fact dental care is free for the first year of the babies life, so prompt mums to make sure they have their annual dental check up booked in, if they haven't already done so.
When discussing weaning (not really done in the early days but HV will pick it up) ensure tooth brushing advice accompanies it.
The freebie bounty/Emma's diary packs, include a baby toothbrush and toothpaste! If it's free people are more likely to use it (and this approach may lessen inequalities)
ANY conversation between GP, HV, or midwife that checks up on maternal health should include a brief reference to oral health. A simple question around 'are you eating ok? Are you looking after yourself, such as showering and brushing your teeth twice a day?' Or something along those lines - (I'm sure you will be better at wording!) could work, as long as it's brief.
Advice for BF mums to stay hydrated, and advise water rather than fizzy drinks, juice etc
Oral health is important but being honest it's not a priority for new mums so any comms near the birth of a baby should be brief, and can then be stepped up when the child is older and starting to be weaned.
The HV should also advise mums on when to register children with a dentist - I've no idea. Is it when the first teeth come through or when the full set is there? A simple addition in the red book could cover this.
Hope that's helpful, and good luck!