I thought it might be amusing to compare memories of our first online chess experience.

In the mid to late 90s I bought my first modem (a 14400 kbit one) after first getting Internet access at work (using NCSA Mosaic for web access), and came across a web-based chess server while very slowly browsing the Internet using Netscape Navigator one evening. If I recall, there was exactly one other person on the server. We played one game. There was no time for any more, as the web page took about 1 minute to load each time (lots of small graphics, slow connection, probably inefficient software). It was quite an expensive game, as I was paying for the phone call. I cannot recall the result, but who cares.

I don't recall it being that bad that late. Things may have been slower to develop in England than in the US.

I looked at the wayback machine and found snapshots of the Internet Chess Clubs starting in 1996. Here is a header from 1997

You have reached:

www.chessclub.com

The world's most active chess club. 
Over 25,000 chess games played daily!

Internet chess records set on May 4, 1997: 2266 people logged in and 307 simultaneous games! 

It looks like they were much better than your memory

The two are not in contradiction, and there were T1 connections at that time (I didn't have one at home). It's funny to think T1 was fast.  Also it's quite likely the server I happened to find was something hacked together on a slow personal server.