No there was a case of a wiemaraner being poisoned on Peckham rye but this was a couple of years ago..
the rat traps popped around the park are very clearly marked and tend to be around the ponds inside the railings
don’t know enough about the stagnant water, but the main pond (and wildlife garden pond) are behind railings so should not be a problem. The other stream areas are clear running water so should be fine?