Size of additional joists to support loft floor

Hope someone can advise me. I have just had a renovation done and so have a mass of nice thick insulation in the loft as per building regs. This is a good height above the existing ceiling joists. I have been previously advised by the builder who did the renovation on how to install a good loft floor. He suggest that I have two existing beams (which have a specific name I have forgotten) running across the top of the ceiling joists. He suggested hanging new beams between these cross beams and then boarding on top of that so the insulation is given enough space beneath - I think I need 250mm for building regs. Thats all good, but is there a specific size of beam I should be using based on the width of the span?

Should I use the plastic stilts method as an alternative to the beams ? I suspect that might be better for reducing cold bridging?

Thanks in advance