google maps
When getting directions from Google Maps, you can set an arrival or departure time. On the Android app, you can set any time you like, but on the desktop webapp, you are limited to only "on the hour" options.
Is there any way to force the site to accept an arrival time of say, 18:30?
Creating a custom map as per MaryC's answer is good if you want something you save permanently or embed and don't mind going through a multi-step process with a different UI to get there.
I also found a quick and easy alternative that uses only the regular Google Maps 'directions' UI.
Basically you just drag part of the path then drop it where it was:
this all depends on algorithms Google Maps usees like:
and also it can be influenced by submitted data Google Maps receives
as you can see on this gif here, the route is always created in sequences and from both sides at once until the link up is created, therefore even a smallest obstacle from (like one-way road due to reconstruction) can lead in different results comparing AB and BA points
more on this topic can be found in answers here from people that work in the field
Best Answer
Time has marched on. Checking some train journeys out of Edinburgh (where OP is shown as based) and elsewhere (UK and abroad) the dropdown has consistently been at half-hourly intervals for me and the granularity 20 minutes (with the forward of backward options) - for both departures and arrivals.