Life insurance is far cheaper the sooner you start. But even though, no point if you're young and don't actually have a real need. You'd be better saving the money towards a deposit or pension etc.
Another point is that it's a lump sum, not a regular amount, so it's a bit of a mis-match to use it to pay rent. It's usually to pay off the mortgage, i.e. a lump sum to pay off a debt.
How long would you need to keep paying rent for until you could get a smaller/cheaper property that you could afford on your own?
Do you/he have pension schemes in place? At the very least, upon death, they'll pay out the current value of the fund, but some will also include a life insurance element too. You/he may already have enough "cover" even if just the pension value, to pay rent for a while.
You need to have a proper evaluation of your respective assets (inc pension values, investments, savings, etc), and ascertain just what you need if either of you dies early, i.e. how many months rent etc. Obviously this evaluation will change with life events, such as buying a house, having children, etc etc.