I recently purchased a 5.5m Humber RIB with a couple of friends that is moored in Kew Marine (right by Kew Bridge), its the Orange one on the end if you ever walk past and are curious!
We're definitely not experts, but from the research I've done and the experince we've got so far I'd say this:
If you intend to go non-tidal, get a 4 stroke
For the tidal part I personally wouldn't feel comfortable with less than the 60HP we have (however I'm sure some will disagree and say you can get away with far less, which is true, I'm merely saying I personally wouldn't want to)
If you are going to be chugging along on the non-tidal part I would definitely consider something with enough seating for everyone, shooting down the river at speed with 3-4 people is fine for an hour or so, but it gets uncomfortable for those sitting on the tubes for a whole 6-8 hour day!
There are loads of Powerboat trainers on the Thames, we all did our courses with Taz Marine and we felt this really helped us
£5,000 should be more than enough, one thing I would say (mainly for the tidal section) is that make sure you allow for lifejackets within your budget, personally on the tidal section I consider these essential
Hope that helps, happy to try and answer any questions you have!