(8) The circumstances referred to in paragraph (5)(c) are that-
(a) the vehicle is parked on a road on which the driving of vehicles otherwise than in one direction is prohibited at all times and its left or near side is as close as may be and parallel to the left-hand edge of the carriageway or its right or off side is as close as may be and parallel to the right-hand edge of the carriageway; or
(b) the vehicle is parked on a road on which such a prohibition does not exist and its left or near side is as close as may be and parallel to the edge of the carriageway. (5)(c) says, (c) elsewhere than in such a parking place or lay-by if-
(i) the vehicle is parked in one of the circumstances described in paragraph (8); and
(ii) no part of the vehicle is less than 10 m from the junction of any part of the carriageway of any road with the carriageway of the road on which it is parked whether that junction is on the same side of the road as that on which the vehicle is parked or not. So you can park on either side of a one-way street, but not a two way road.
Ian