Do www.eurostar.com do add-on fares? Polegate-Brussels? Think not but...

>>I assume she just purchases this ticket at Polgate on the day she leaves?
And returning on the Sunday when they are coming back from Brussels to St Pancras--the same? (ie just buy their ticket on that day )<<

For a definitive answer, there's no substitute for checking on the National Rail website for the fares at different times and different dates - see if the fares are any different booking for today or in several weeks' time. Also check if travel is at off-peak times - that might give greater flexibility cheaper than the Anytime fare. Internet-savvy teenagers might be good at that..

The 30 day open return ticket is bought for the day of outward travel and the return ticket then sits in your pocket until you come back. If you buy a single out and a single back in London on the Sunday it will be more expensive.

I've never bought one but my daughter claims you can't get them from the machines which is why I suggested asking at the station. Or at Eastbourne Station if she can get there beforehand.