Would tax be due on the difference?

I am thinking of renting out my own home and then renting something smaller. Would I only be liable for tax on the difference in cost between the two properties as I do need somewhere to live?

I am sorry but what you have written is not correct. You will be taxable on the full amount of your rental income, even though you have to pay rent elsewhere to enable you to rent out your property. See www.hmrc.gov.uk/manuals/bimmanual/BIM37928.htm that you paying your own rent is deemed a personal matter, and not a business expense.