Can you still have people on furlough leave full-time after 1 July 2020?

Yes. You can continue to fully furlough employees until 30 September 2021 (but from between 1 August 2020 and 31 December 2020 and from 1 July 2021 you need to contribute to the cost). If on full-time furlough, employees continue not to be able to undertake any work for you. As before, they can undertake training, or volunteer or work for another employer or organisation (if contractually allowed).