Investment trusts themselves are publicly traded, they're closed-ended funds with capital raised once on launch - sort of like pooling private equity, but you can then sell your stake.

The public listing is of the company, whose business happens to be investing, so though I've never looked I don't see why CFDs & derivatives wouldn't be available.

Venture Capital Trusts (VCTs) are similar (perhaps a subset?) but focus on earlier stage companies (clearly) in exchange for a tax advantage for the initial investors - but not for those who subsequently purchase shares in the VCT itself from them.