Can I lay a new carpet on top of existing carpet?

[MikeNumberOne]

The house I just moved into came with carpets. I decided to replace the lounge carpet but when I tried to take it up it appears to have been glued in place on a concrete floor. It made such a mess with backing and bits of carpet stuck fast onto the concrete that I gave up. I think the old carpet was foam backed but I'm not 100% sure. If it is OK to carpet over an old carpet, is it best for the new carpet to be hessian backed, felt backed, or something else?

[Chrisbond]

Hi,
It is best to remove the old carpet as the new carpet can move around instead of lying still. Hessian backed carpets are usually harder wearing but need and underlay, foam backed carpets can be laid directly on a hard surface.
Regards