We will be fitting new 22mm pipes throughout, will this help to
alleviate this?

Quite the opposite. The throughput of a standard combi boiler is so low that
no more than 15mm is needed unless your mains water is very low pressure.
However, the 22mm pipe has twice as much water in it per unit length, so it
takes twice as long to clear out the cold, given that the flow rate is
limited to a fixed low value, around 11.5 lpm, which 15mm is very capable of
supplying at mains pressure. Gravity systems needed larger pipes because the
tank fed nature leads to very low pressures, so didn't have the "push" to
squeeze through smaller pipes.

Christian.