Grouping and selection of amendments is done by the Chair of the committee. It is entirely at their discretion and by convention is not questioned once it has taken place. The link does not make clear if if the selection can be questioned either privately or publicly prior to the debate.
Selection and grouping is the Chair’s decision. You should not question it during the debate.
The chair varies based on the type of Bill.
For a public bill committee, selection and grouping will be carried out by the MPs from the Panel of Chairs who’ve been chosen to chair the committee. For a Committee of the whole House, the Chairman of Ways and Means (the principal Deputy Speaker) will carry out the selection and grouping. For report stage, the Speaker will carry out the selection and grouping.
This is all detailed on the Parliamentary website.