Peter,
Do not understimate the power of drafting, in a large group. We are lucky in that our club we actually practise and learn group/bunch riding discipline and as part of the sunday club run we will practise elements of it eg team time trial, through and off, chain gang type rotation as part of the club ride. We have quite long, flat stretches of quiet road on our training routes and one day we all worked together going through and off just to see how far we could wind it up. You would be surprised to learn that it is not that hard to bomb along at 26, 27,28, 29 even 30 mph on the flat for a while as part of a group. Ok it is tough when it is your turn to take a pull at the front but you only have to really dig in for a bit.
If you ever have the opportunity to watch a local road race (does not have to be elite TDF type stuff) you can get quite close to the action and the draft as a large bunch goes by is amazing, you can feel yourself being sucked along.
The reason I am saying this is that more or less all my previous riding for the past two odd years was done with the CTC at a leisurely 12.50 mph average. OK I have built up a base of slow steady miles but my stretching the legs average was around 14-15mph at best and I wanted to go a little quicker so I looked for a race club (this was April this year). Because I had ridden previously, the group I got put into averaged between 16-18 mph and yes towards the end of some of the rides I was struggling a bit but each week I got better and stronger and in fact now on some of my rides home from the club run my average speed actually increased slightly. I am at the point now where I am toying with popping along to the next group up who average 18-20 over about 50 miles with a 22-24 mph average sting in the tail on the way back to the club house.
As a 40 year old ex 20 a day smoker, who did not really think about fitness until his late 30's heck if I can do it and keep up then anyone can.
Your original question was in effect am I quick enough to join a club, the answer is you will only ever be able to truly answer that if you go along and actually find out. Any club worth anything should be pleased to receive a new member and even if you are not quite quick enough just yet should give you every encouragement you need to bring yourself up to speed.