Reading have played Thames 2 times in competitive football, winning 1, drawing 1 and losing 0, first meeting on 10 Oct 1931 and most recently on 9 Jan 1932. Every meeting is listed below.
| Date | Season | Competition | Venue | Opponent | Score | Scorers | Att |
|---|---|---|---|---|---|---|---|
| 10 Oct 1931 | 1931–32 | Third Division South | A | Thames | 0–0 | ||
| 9 Jan 1932 | 1931–32 | Third Division South | H | Thames | 5–1 |