I want to utilise unused loft, for storage. Do I need to strengthen the joists, and if so, how?

You need a local code to guide you and probably a local contractor to look at the existing plan to judge its soundness,there are a lot of possibilities that a CONTRACTOR,or even the local code enforcement officer can suggest for your needs.

Hope this helps,
Ken

Well need to know the span you have and the wideth of the joist you have there now