The micro- and macroscopical features fit well.
Coulour is variable, depending on the stage of development from light violet (immature) to dark violet (mature) and even black (overmature).

The habitat convinced me also.

I found Peziza boltonii on 01-03-2001 in the centre of Maastricht in the most southern part of the Netherlands, it was the first record of this early species.
It grew on calcareous sandy soil along a path next to the old city wall between the bricks. Not a place where one expects to find fungi of any kind. In the past the builders of the wall used lime mortar as cement and this proved to be very interesting for P. boltonii as well as Tulostoma brumale and Omphalina rickenii which both could be found on top of the brick wall between moss in the joints. All these species seem to prefer calcareous soil which can be found in this part of the Netherlands or in the coastal region.
Since 2001 P. boltonii is working its way up north and has mainly been collected along the Dutch coast. Your find near the sea fits perfectly with this trend.

Hope this will help.
All the best!

Ron