I would say a minimum you must get is 10 HP.
I'm sailing on Thames, my boat is kept on a swing mooring. When the tide reaches 3-4 knots, and this is not unusual, I struggle to make 200 yards from my boat to the shore. My dinghy is about 10ft with a Tohatsu 2.5 HP, and being alone is sometimes quite frightening how fast and strong the tide can be.
Otherwise, I have an inflatable 3.65m which is rated 20hp max. It's a aluminium solid floor and weight about 120 kg, plus myself and some gear and I would not go for below 10hp. I actually have a 20 HP and a 25 HP for this boat.
From my experience on Thames, I would suggest to have some good power reserve, for your own safety. The navigation is busy here, tide is strong and sometimes you really need to put a WOT to stay safe. Cheers