  We examine the constraints on the trilinear Higgs coupling $\lambda$ that
originate from associated ($Vh$) and vector boson fusion (VBF) Higgs production
in $pp$ collisions in the context of the Standard Model effective field theory.
The 1-loop contributions to $pp \to V h$ and $pp \to jj h$ that stem from
insertions of the dimension-6 operator $O_6 = - \lambda \left (H^\dagger H
\right )^3$ are calculated and combined with the ${\cal O} (\lambda)$
corrections to the partial decay widths of the Higgs boson. Employing
next-to-next-to-leading order QCD predictions, we analyse the sensitivity of
current and forthcoming measurements of the signal strengths in $Vh$ and VBF
Higgs production to changes in $\lambda$. We show that future LHC runs may be
able to probe modifications of $\lambda$ with a sensitivity similar to the one
that is expected to arise from determinations of double-Higgs production. The
sensitivity of differential $Vh$ and VBF Higgs distributions to a modified
$h^3$ coupling is also studied.
