Have posted before on these threads and have been quoted on the podcast - I'm the UK poster who brought up the Eurotunnel /Eurostar service opening in 1995 and mentioned how easy it would have been to travel to continental Europe.
I remain convinced that there was purpose in Marion's trip to that corner of the UK. It is hard to get across to non-Brits how strange it is to dedicate a long visit to a rural area with small towns. Nearly all Australian visitors (and those from other countries too) want to see London, York, Edinburgh, Stonehenge, the Lake District.... although Kent and East Sussex is very pretty, it's really not top of most people's lists. Unless you chose that particular location for other reasons of course.
On the marriage thing - not convinced. In the UK we have had the system of proclamation of banns in church for centuries, and if you want to marry in a civil ceremony in a register office, you have to give notice. You have to give 28 days notice in person (both parties), and have been in the country for 7 days before you give that notice, so 5 weeks total. Registrars are sticklers for the rules and would not have deviated from them. They also ask to see identity documents and interview you to make sure you understand what is going on, and that you're not being coerced. If Marion entered the UK on a tourist visa (likely) then she's not allowed to marry under the conditions of that visa, she'd have had to apply for a fiancee visa to marry an EU national in the UK. Registrars being employed by the government are not going to ignore those laws. There's just not enough time for Marion to have arrived in the UK at the end of June and organised a wedding for the first week in July. I am not sure what the rules are in Luxembourg but nowhere in Europe is like the movies where the characters say "Let's go to Vegas!" and are married the same day.