Short answer. Yes. You may demand that the bank owners permit the construction, but only after payment of damages, including those caused by the new easement to such owners and to the other irrigators — the compensation duty extends beyond the bank owner to everyone else who irrigates from that stream.
What the law says
after payment of damages, including those caused by the new easement to such owners and to the other irrigators
Civil Code, Article 647 — Stop Locks and Sluice Gates. Read the full provision →
The right to build comes with a price attached
The law lets someone who needs to construct a stop lock or sluice gate to irrigate or improve their land demand that the owners of the banks allow it. That right is not free-standing, though — it is conditioned squarely on payment of damages first, before anything else. The structure benefits your land, but the law does not let you impose it on others without compensating them for what it genuinely costs them. That duty binds you as the person constructing the works, not the bank owners who merely tolerate it.
The bank owner is not the only one entitled to compensation
This is the part that answers your question directly: the damages to be paid are not limited to the bank owner. The provision expressly covers damages caused by the new easement to such owners and to the other irrigators. Anyone else drawing water from the same stream whose irrigation is affected by your stop lock or sluice gate is entitled to compensation as well, not merely whoever formally owns the land the structure physically happens to sit on.
Why other irrigators are affected at all
A stop lock or sluice gate changes how water moves through the stream, which is exactly why the rule reaches beyond the bank owner. Other people irrigating from that same stream can have their water supply reduced, redirected, or otherwise disrupted by a structure built upstream or at a control point, even though they own no part of the bank where it stands — which is exactly why the law treats their loss as compensable too, not just the loss suffered by whoever formally owns the affected bank.
Payment comes before construction, not after
The wording places payment before the permission is exercised — the right to demand that the structure be allowed follows after payment of damages, not the other way around. Practically, that means working out and paying compensation to the bank owners and the affected irrigators is a step to take before building, rather than something you can simply promise to settle only if a dispute happens to arise afterward.