Yes, you'll need some insulation underneath you.
Mats insulate OK, but they can migrate out from underneath you during the night if you are a restless sleeper, so you wake up cold, with the mat up the side of the hammock. You don't need a soft/thick mat, so closed cell foam mats
similar to this are fine, and can be found in Wilkos and similar places, though it's not really the season for finding one locally. I'd be inclined to consider two taped together edge to edge in order to get round the moving out from under problem. It would be a bit bulky to carry though.
Some hammocks have pockets to keep a mat below you (a double-layer over the bottom).
Some people use quilts suspended underneath the hammock on elastics (needs to be a relatively close fit, rather than hanging loose with a big gap).
Have you considered using a bothy? (all closed due to covid)
Another thought - there may be a suitable double-side removable tape you can use to keep a mat in place.