One of the biggest and easiest is long term normalisation of their policies - anything that seems radical needs to be given time to enter into public discourse through discussion, small scale trials, and joined up thinking. It's easy to dismiss the idea of free broadband for all as some radical commie plot if it seems to come out of nowhere but it's a pretty small thing that will make a huge difference to the economy and to potential equality of opportunity. With the right positioning the public can change opinion and comfort levels pretty quickly. Ed Miliband, for all his faults as a leader, always knew this and is making a good fist of it in his later political career (this isn't about his actual politics it's about how he gets across his views and policies).
It will be harder for Labour than the Tories because they do not have a favourable press and it's unlikely anyone standing on a Labour platform will (if Starmer actually kept to the platform he stood on the media would generally be unfavourable) but it is not impossible.
Tory lite is not an option because full fat Tory is there and so why would anyone go diet? And, more importantly, Tory Lite is no good. It will not make the country fairer, or more welcoming, or better for cyclists, or better for the lowest incomes. Partisan politics isn't a bad thing, compromise isn't some great political weapon.