<p>In this work, a Hybrid High-Order Finite Element Method (HHOFEM) is evolved and rigorously investigated to approximate a family of initial boundary value problems (IBVPs) exhibiting singular perturbations. In the HHOFEM scheme, each mesh cell uses polynomial functions in the interior and separate polynomial values along its edges, allowing the method to accurately capture steep boundary and interior layers. The HHOFEM framework relies fundamentally on local reconstruction operators and a robust high-order stabilization mechanism. The main difficulty for handling the singular perturbation problems (SPPs) is the solution’s multiscale behaviour, where sharp variations appear close to the domain boundary, giving rise to pronounced boundary layers. When dealing with practical models, it becomes highly challenging to predict or characterize the structure and behaviour of the boundary layer. This study examines error analysis on both a priori layer-adapted mesh and a posteriori adaptive mesh. The a priori case assumes the boundary-layer shape is known and uses it to design the mesh in advance. The a posteriori approach instantaneously identifies the layer behaviour via adaptive mesh refinement. The temporal discretization employs the backward Euler scheme on a uniform grid, and the analysis demonstrates parameter-uniform convergence in an energy-type norm, with comprehensive numerical experiments verifying these findings and showing that the method reliably and efficiently captures layer features on both types of meshes. Finally, numerical experiments are performed to assess the performance of the proposed HHOFEM scheme in comparison with the closely related weak Galerkin FEM (WGFEM).</p>