You have been on the site for 7 years and are a member of 19 clubs...
How can I take part in team matches on chess.com?

I have only been active here for about 6 months and I don't think any of those clubs have team matches.

Team UK play regular matches as do Team England. You could also apply to join the team of whichever city you are based in/closest to or the county you live in as many play in city leagues/county championships.

Are you in the the team? If you are then I would be interested in taking part but I couldn't really see any information about matches on the team pages

I see you are already in Team UK... go to the club page, scroll down, then click daily matches. Here you will see all the matches which are currently open for registration. There is a 1WL u1200 match open with plenty of spots available which you could join. Same way to find open matches for any other club you are a member of. That and also clicking upcoming events at the top of the club page.
How to find teams to join?