Can I transfer existing retirement savings in to a plan?

Yes, you can, although this may depend on the value of the pension you are looking to transfer.  There are rules requiring you to have received advice from a qualified financial planner for pension plans of a certain type and size.

The value of pensions can fall as well as rise, you may get back less than you invested.

Transferring out of a final salary pension is unlikely to be in the best interest of most people.