Oliver can probably correct me where Im wrong, but I don't think that turning across the flow of traffic dispenses with the requirement to make sure there's nothing coming the other way.
The relevant rule in the HC is rule 211 (scroll down):
It is often difficult to see motorcyclists and cyclists, especially when they are coming up from behind, coming out of junctions, at roundabouts, overtaking you or filtering through traffic. Always look out for them before you emerge from a junction; they could be approaching faster than you think. When turning right across a line of slow-moving or stationary traffic, look out for cyclists or motorcyclists on the inside of the traffic you are crossing. Be especially careful when turning, and when changing direction or lane. Be sure to check mirrors and blind spots carefully.
181When turning right at crossroads where an oncoming vehicle is also turning right, there is a choice of two methods
[]turn right side to right side; keep the other vehicle on your right and turn behind it. This is generally the safer method as you have a clear view of any approaching traffic when completing your turn
[]left side to left side, turning in front of each other. This can block your view of oncoming vehicles, so take extra care. Cyclists and motorcyclists in particular may be hidden from your view. Road layout, markings or how the other vehicle is positioned can determine which course should be taken
(Illustrative drawings not reproduced.)
Note, though, that these rules are advisory only.
Every cyclist should know their HC, or, better still, carry it with them sometimes. It is very useful in resolving a potential dispute with another road user.
The relevant rule in the HC is rule 211 (scroll down):
http://www.direct.gov.uk/en/TravelAndTransport/Highwaycode/DG_069858
http://www.direct.gov.uk/en/TravelAndTransport/Highwaycode/DG_070332
Note, though, that these rules are advisory only.
Every cyclist should know their HC, or, better still, carry it with them sometimes. It is very useful in resolving a potential dispute with another road user.