A local cycle club started up last year & when I asked what speed they would be riding at I was worried by the average 17mph figure, I used to manage 14/15mph at best. Anyway went along & managed it. As others have said you'll easy gain a couple of mph just by being towed along by the group

After a few group rides at a faster pace I found myself cycling faster even when alone & have now done a few solo rides with 20mph average which I would have though impossible 12 months ago.
I'd say join the club ride & see how you get on, what's the worst that can happen? You'll maybe get dropped, but if it's a friendly club someone will drop off with you so you're not alone
