What happens next depends on the outcome of the consultation (and the wider political landscape)
The government will review the responses and then formally respond, setting out what they intend to do next (either legislate to make changes, or leave things as is, perhaps with some new non-statutory guidance).
If they decide to do something that requires legislation, the government will need to draft a bill and then bring it to Parliament. Most of Parliament's time is taken up with Brexit matters at the moment, so finding space on the work schedule could be tricky, especially if it's believed to be contentious (because the government doesn't have a majority, and will want to use their good will to get through stuff like Brexit rather than this). This is when MPs and the Lords will debate the provisions in detail and get to vote on them. So any actual change could be months and months and months away yet.
Yes, school holidays reduces the time for people to analyse and consider and consider the proposals, particularly groups that might want to meet to discuss them and organisations that might want to ask their membership for their views. I suspect that is why the consultation period is longer than the standard 12 weeks (though not sure that the extra three weeks really helps, given how busy the back to school period is for many)