Well, for me anyways ...

- I can't assign settlers to tasks
They'll say their usual line but then never actually do anything. Tested with both food and guard posts.
Once i assigned a settler, they just stand in whatever spot they were in and stop moving completely.
And then the assignment undoes itself and they show as unassigned again.
Even worse, each settler i tried to assigned is *removed* from the settlement count, i started with a count of 7 and now i'm at 0.
Thing is, they're all still on the bridge, they just can't move anymore.

- Churchill turns into Dogmeat
While building on the bridge, Churchill kept getting in my way so i tried to dismiss him only to realize i could only dismiss him to the same settlement (haven't unlocked any other yet).
I did that and he sat down in front of the workbench.
When i was ready to go out again i asked him to follow me and fast traveled somewhere else.
Upon arrival, his body was replaced with Dogmeat (But he still was labeled as Churchill).
I fast traveled back to the bridge and there he was still sitting in front of the workbench so now i have *two* dogs named Churchill, one of which looks like Dogmeat.
And both are interactable and react to my commands.

Yeah these are known issues.

I'm surprised your settlers stay on the bridge though - mine teleport into the water below. Bye bye Beefy!

Yes, the settlement is bugged but at last you can store junk there and build workbenches so you don´t have to carry everything around anymore.

There is a fixed script for churchill currently on nexus available (no mod, just a script) so he follows you again. If you already got dogmeat spawned it´s no problem, he will just stay at the place when you took churchill again and don´t make any problems.

I am also having this issue at Covent Garden, so it's not just London Bridge.

It does work but, it takes a long time to happen.

In FO4 you get instant results when you assign a settler to a crop.

In FOL it seems to take several in game hours or even days for them to actully start doing the task.

Try selecting the settler and point him/her to a plant and you'll hear 'okay'.
Them select them again and use the 'Move' command and send them to the London Bridge Settlement (even though they're already there).
You should see their icon change and they are allocated to farming.

Settlers still need fixing and I believe the devs are aware of the issues.

Is there a way to get this settlement if anyone of the original inhabitants is dead?
When i first came there everyone was attacking me at sight and i fought back....