Can't speak to the situation in the UK, but in the US all the big sites, such as FlightRadar, FlightAware, etc. rely on both a paid-for FAA radar data feed as well as host of independent, primarily amateur, ADS-B receiver sites. Thus you will get both ADS-B and non-ADS-B equipped traffic.
Obviously, if the traffic is not within a radar or amateur ADS-B coverage area, and helicopters are often low enough for that to happen, it won't be seen.
The FAA also has a program where you can opt your aircraft out of the publicly accessible FAA feed. It need not be a military or public safety aircraft to opt out. However, such aircraft, if ADS-B equipped, cannot hide from the amateur ADS-B receiver network. Even more interestingly, there are now networks of amateur MLAT stations that can geo-locate regular Mode C and older, non-ADS-B Mode S transponder emissions, not that such equipment will remain relevant for very much longer in the US given the US ADS-B mandate.
One thing that is not clear is whether or not the big websites like FlightRadar are given a "do not publish" list by the FAA. They can't stop a local ADS-B receiver operator from seeing everything that is around them, but they don't have to forward that information when it is uploaded to FlightRadar from one of the amateur receiver sites.
I've dabbled in this arena, and have built a dual frequency (978 and 1090MHz) ADS-B receiver unit. I can easily see all ADS-B equipped aircraft for many miles around, depending on altitude, of course. So when the Black Helicopters are coming to get me I'll be able to see them coming
You can buy your own, commercially made, ADS-B receiver, or construct your own if you are handy with a PC, and not be subject to big website filtering, nor the multi-minute delay they put into their feed for "security theater" purposes.