STATUTORY LOSS OF NOTICE (PILON) - deducting outgoings when self-employed during notice period

chantaspell

Hi! Have had a good search for this but can't find the answer. There is a government helpline but it is closed.
I was made redundant after 12 years permanent contract and my PILON period has come to an end and I can now claim STATUTORY PILON  (or claim for loss of notice, as they call it on govt website). The company themselves claimed total insolvency and therefore haven't paid a penny in redundancy or pilon themselves. The tax payer is coughing up (thanks guys!).
After being made redundant I immediately picked up some free-lance work. As I understand it, any work carried out/moneys earned in the PILON period must be declared and will (to some extent) be deducted from your loss of notice pay. Also, as with self-assessment tax, you can deduct your outgoing expenses from your earnings . My question is this: What outgoings can I deduct?
For example, the self-employed work I did required new IT hardware which was essential and only used for work. I assume I can deduct this expense. I also assume I can deduct the hosting costs of the website I set up.
Can I also deduct a proportion of my Internet costs as I use internet primarily for work (obviously only a % of, as I don't only use internet for work)?
Can I deduct a % of my heating bill for the extra hours I spent at home?
As far as I can see, there is no specific advice on this and no way of contacting the govt agency responsible. Should I treat it as if I were calculating profits for self-assessment? 
Any help or suggestions as to where I can find the answer to this are very welcome! And I hope it's not a daft question. 
Many thanks!