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Abstract We present a complete (non-redundant) basis of CP- and flavour-conserving six-dimensional operators in a two Higgs doublet model (2HDM). We include ℤ 2 $$ {\mathbb{Z}}_2 $$ -violating operators as well. In such a 2HDM effective field theory (2HDMEFT), we estimate how constraining the 2HDM parameter space from experiments can get disturbed due to these operators. Our basis is motivated by the strongly interacting light Higgs (SILH) basis used in the standard model effective field theory (SMEFT). We find out bounds on combinations of Wilson coefficients of such operators from precision observables, signal strengths of Higgs decaying into vector bosons etc. In 2HDMEFT, the 2HDM parameter space can play a significant role while deriving such constraints, by leading to reduced or even enhanced effects compared to SMEFT in certain processes. We also comment on the implications of the SILH suppressions in such considerations.