They don't dictate policy they advise, but as we have seen where those who do decide policy ignore the advice, it goes wrong. We know from the released minutes SAGE advised that to allow a 5 day relaxation at Christmas would risk a surge in hospitalisations that could overwhelm sections of the NHS. Unofficial SAGE was of the same opinion. Didn't take a genius to work that out as hospitals were already seeing a rapid increase in admissions prior to Johnson promising a 5 day Christmas easing, he was going to have to do a U turn. In Bristol the Nightingale Hospital was already being used in order to free up wards in two other hospitals for the ongoing covid surge.
A full week before Hancock announced this more infectious strain, the BBC on Radio 4 interviewed a doctor in Kent who said that the virus was not doing what it should be and that a more infectious strain was suspected to be involved. The Govt. knew this, and yet they waited for the 'structure' of the new strain to be confirmed before making the announcement well after most people had made their Christmas plans. Trying to be popular does not make for good decision making.
Regarding the comments up thread about using Army and Police to enforce lockdowns, that was always in the gameplan, we used it in the 1998 Pandemic Exercise. Mobile road blocks, main route closures in and out of high infection areas. We used Oxford and Milton Keynes as the exercise examples. This government has hardly touched the emergency powers it could use, imagine the whining if it did.