The bottom line is that IF its tidal then there's a small chance you may be able to detect legally depending on Crown permits (but it would only be between the high and low water mark which would be very small on a river such as you describe).
Otherwise the river bed will be owned by the adjacent landowner up to a point called the median line, (centre of the river), unless they own both banks in which case obviously they own the whole river. So you still need permission - just because its a river does not mean that you can detect it.
You also have to be aware of potential damage to fish spawing areas, so also seek advice from the environment agency as some river beds are protected.
1. Check who fishes the area. Even if the powers that be gave you permission if it's a club-managed stretch of water you'll be as popular as poo on a blanket. It would be a brave man that peed off a group of catapult wielding, maggot throwing fishermen.
2. If there are gravel shallows check if the river holds barbel. Even if the shallows are not protected you would be more responsible not to disturb them during the closed season (just finished), or better still not at all.
3. Know your disease symptoms. A town river has two lovely ingredients - lots of broken glass and rats.
4. If it does turn out to be OK then wade the river first with a wading stick. The brook (4m wide) near here has beautiful sunlit gravel and sand shallows. As you go go under the trees it has sumps over 2m deep.
All sounds like a good idea but plenty of research to do first.