There's no license required to own a marker as such, in the UK. We have some fairly strict firearms laws, but they don't really get applied to paintball as such.
Semi-auto only (one trigger pull = one ball - I'll say more about this later), firing less than 330fps.
Firing at a velocity higher than above using a standard paintball would cause your marker to be deemed a firearm.
As far as firing modes are concerned, the rule of law stipulates that a marker should fire one ball per trigger pull. Accidental double firing does not constitute a criminal offence (e.g. double feeding, or trigger bounce). Ramping is a legal grey area. Although technically breaking the law no court has yet made a judgement on it (and we should probably avoid even taking it to court if possible). To the best of my knowledge, when the Millennium Series is in London, they do use the Millennium ramping mode (10.4bps, following 6 trigger pulls, then maintaining 6 trigger pulls per second). I could be wrong on this, but I haven't heard any differently.
Basic common sense is also useful. For example, don't be waving your marker around in public. The general public here are probably not aware that you're waving a paintball marker and could confuse it for a real weapon. This goes double for milsim.
Break your marker down into as many reasonable component pieces as possible. Remove hoppers, air system, barrels. We aren't talking about taking the thing to bits. Think about how the marker comes to you in the packaging and you'll be on the right track.
Carry markers in the trunk of your car, preferably in a lockable flight case. This isn't necessary, but if you're stopped by the police it shows that you're making an effort to ensure that it can't be accidentally discharged. Keep air and paint separate from the marker.
If the police do stop you, be open and honest about what's in your vehicle/bags. Explain that you have a paintball marker on your person/in your vehicle. They will likely ask you if you are carrying any ammunition and/or compressed gas. It is not unreasonable for them to ask to see it, though common sense should prevail if you're in a public area.
It's mostly common sense stuff. Hope this helps!
edit: almost forgot the UKPSF is a good resource: http://www.ukpsf.com/paintballlaw.php