It can't be done safely on your budget. To reduce costs look to take less people out and forget the Channel Islands, just stay around the UK mainland.
To take 6 people across the Channel you'll need 6 proper seats which normally means a 6.5-7.5m RIB and a 200-250hp engine to get you in and out of the big stuff if it kicks up.
However £6k should get you a nice 2 man rib which you will have loads of fun with.
Ribeye are the smallest boats with the most seats but they do command a high price, maybe twice your max budget to get an old one
If you're on a tight budget, also consider storage, fuel and servicing costs.
I hope that helps a bit