Best place for chub near to Aylesbury is the Upper Great Ouse which flows through Buckingham. This is prime chub water. I ahve fished it often below Buckingham on the Buckingham and District AC book.
The chub in the Ouse here are big, yet they are very crafty. A this time of the year you will have to stalk them. That means dressing in camouflage and crawling on your stomach. If the river is clear, that means you can see them, especially if you wear polarised specs. And in most cases they can see you if you are not careful. If they can see you you won't catch anything.
Take an Avon style rod, load your reel with 8lbs line, tie on a number 4 hook and take a little bag full of bread, a few lobs, some cheese paste or catch yourself a few slugs in the early morning dew wetted grass. You will also need a landing net of course.
When you get to about 15 yards of the river get totally prone on your stomach and crawl.
If you see a chub, cast a bait to it. If you haven't scared the cub it will invariably take the bait first time. Beware if you use a slug. They take it with tremendous force.
The hang on for dear life and heave.
The chub in the Upper Ouse average over 41/2 bs.
If you want barbel you will have to try the Thames or the Kennet. I have not fished these rivers all that much so I don't feel qualified to advise. I am sure someone else can.
Its a river that holds many surprises yet is so under fished. My favorite river by far