One of my DCs had a very misshapen skull as a baby.
Our paediatrician told us that the NHS will only treat misshapen skulls in babies - this would include babies with flat heads - if the doctors think that the issues with the skull are likely to affect brain growth and development. One thing they were concerned about with our baby was the possibility that the skull plates might have fused too early, this is rare, but is something that can mean the baby's brain doesn't have room to grow normally.
If they think the brain will be able to grow normally, then the skull being partly flat or otherwise misshapen is considered a cosmetic issue and things like helmets to treat it isn't something that the NHS will pay for.
This may vary between different areas in the country, and our experience was several years ago, so the policy may have changed, but I wouldn't count on the NHS funding a helmet.
In any case, if you have concerns, I'd advise you to speak to your GP about it, they'll be able to refer you onto a paediatrician if they agree it's something to be concerned about.
In our case, after some monitoring, our baby's skull shape was ultimately considered a cosmetic issue by the paediatrician, and our baby's head shape grew more normal as baby got older, particularly once baby was sitting, then crawling, and able to roll over in the cot at night. Our child is now 5, and with a normally shaped head.