How to approach my local Shul about a visit?

I’m a born-gentile looking at becoming part of the community (Edit: not using the ‘C’ word cos I don’t wanna ding anything as my post is not about that lol), and I would like to visit my local Shuls to speak face-to-face before approaching the Biet Din in London.

The Jewish community in my area is quite teeny tiny (we’re talking 0.1%), but there are four shuls and one ‘progressive temple’ within a five mile radius, two of them are within 1.5 miles in fact, so there’s definitely something of a community to join, which is nice.

I know I have to ask permission to visit, being an ‘outsider’, but how might I word my email? Should I just ask ‘can I visit please’ or should I lay out my reasons and interests/intentions without them asking? Do I ask to visit on Shabbat, or go in the week when it’s not a particular event day?

Sorry if it’s a dumb question! Thank you, and I hope you all had a peaceful and safe Rosh Hashanah.