I see many people at work who have been made redundant and the experience can be akin to bereavement. That may sound depressing but it is not meant to be. I use that analogy to explain that there is a progression; of immediate distress, anger, a period of adjustment and then a process of resolution.
My best advice is to view this as opportunity. Work at looking for work (as someone else said; set your alarm, set tasks for every day) but also perhaps take the opportunity to do other things. To read some books you've always put aside, to get fit, to fix the broken garden fence, learn to make bread, to re-connect with friends or family. Do a bit of volunteering, apart from the obvious benefit it may also connect you to a new social group having left the workplace. Most important take time to consider your future in a measured way. It can be hard to do that in the immediate aftermath but my experience is that decisions taken in great haste in these situations are not always the best. You do have time with your exit payment, and even just a few weeks breathing space may give you perspective and also clarity on what you actually want and the options are available to you.
A practical suggestion. You might be able to access some training at your local college in some of the skills you mention as lacking. If you sign on at your local job centre as looking for work it is possible that you may get financial support with this or at least pointed in the correct direction. I think there are also UK Govt schemes for helping people who might be considering setting up as self employed. I don't know the details but I believe there is a bit out there. Your Bank might also have resources too.